After examining the briefs and appellate record, this panel has determined unanimously to grant the parties’ request for a decision on the briefs without oral argument. See Fed.R.App.P. 34(f); 10th Cir.R. 34.1.9. The case is therefore ordered submitted without oral argument.
Plaintiffs-appellants Patrick and Olita Jo-jola filed this suit, under 42 U.S.C. § 1983, on behalf of their daughter Bridget Jojola, *490against the Socorro School Board and several of its employees. They sought relief against the defendants in their individual and official capacities for alleged violations of Bridget’s constitutional rights. The district court dismissed the entire action for failure to state a claim, and the plaintiffs appeal, challenging only the district court’s order dismissing the individual capacity suits against defendants Chavez, Hayes, and Fraissenet. Our jurisdiction arises under 28 U.S.C. § 1291, and we affirm.
BACKGROUND
In 1991, Bridget Jojola, who was then a fifteen-year old tenth grade student at Socorro High School, was forcibly molested by defendant Chavez, the school’s custodian. While Bridget was walking from a classroom to the girls rest room, during a regular school day, she was approached by Chavez, who led her into a dark, vacant classroom where he molested her. Chavez later pled guilty to one count of criminal sexual penetration, a second degree felony, and was sentenced and committed to prison for this crime. At the time of the attack, defendant Hayes was the principal of Socorro High School and defendant Fraissenet was the Superintendent of the Socorro Consolidated School District. The plaintiffs initiated this § 1983 action, claiming the defendants’ conduct violated Bridget’s constitutional rights under the First, Fourth, Ninth, and Fourteenth Amendments to the Constitution, as well as alleging violations of state law.
The district court granted the defendants’ motions to dismiss the federal claims, concluding the plaintiffs failed to demonstrate that defendants Hayes and Fraissenet knew Chavez had engaged in a pattern of violating female students’ rights to be free from sexual abuse by school employees. The district court also concluded the complaint failed to state a claim against Chavez because his actions were not performed “under color of state law.”
DISCUSSION
We review de novo the district court’s dismissal of a complaint under Fed. R.Civ.P. 12(b)(6) for failure to state a claim. See Gagan v. Norton, 35 F.3d 1473, 1474 n. 1 (10th Cir.1994), cert. denied, — U.S.-, 115 S.Ct. 1175, 130 L.Ed.2d 1128 (1995). ‘We ‘must accept all the well-pleaded allegations of the complaint as true and must construe them in the light most favorable to the plaintiff.’ ” Id. (quoting Williams v. Meese, 926 F.2d 994, 997 (10th Cir.1991)). Dismissal is only appropriate when the plaintiff can prove no set of facts to support a claim for relief. See Noland v. McAdoo, 39 F.3d 269, 273 (10th Cir.1994).
I.
Plaintiffs first argue their claims against Fraissenet and Hayes should not have been dismissed because they have shown Chavez engaged in a pattern of violations. Plaintiffs further argue that even if Fraissenet and Hayes did not have personal knowledge of the specific incidents, at a minimum, they had constructive notice of the incidents from other subordinates. We are not persuaded.
■ “[Liability under § 1983 must be predicated upon a ‘deliberate’ deprivation of constitutional rights by the defendant,” and not on negligence. Woodward v. City of Worland, 977 F.2d 1392, 1399 (10th Cir.1992), cert. denied, — U.S.-, 113 S.Ct. 3038, 125 L.Ed.2d 724 (1993). Therefore, to impose personal liability on Fraissenet and Hayes, plaintiffs must allege, and prove, defendants actually knew of and acquiesced in Chavez’s behavior. See Id. In order to show actual knowledge by Fraissenet and Hayes, the plaintiffs must prove “the defendants received notice of a pattern of violations of female students’ constitutional rights to be free of sexual abuse at the hands of the school district’s employees.” Gates v. Unified Sch. Dist. No. 449, 996 F.2d 1035, 1041 (10th Cir.1993).1 The plaintiffs attempt to show Fraissenet had actual knowledge of Chavez’s improper contact with students based on his statement to the plaintiffs that *491problems involving Chavez had arisen prior to the attack on Bridget Jojola.2 The complaint specifically alleged a parent had informed the junior high school principal that Chavez had put a hole in the wall of the girls’ locker room through which he watched girls using the facility. The plaintiffs also alleged rumors, had circulated at the school concerning Chavez’s improper sexual behavior. Finally, the plaintiffs alleged Fraissenet and Hayes should have been alerted by the rumors that they needed to investigate whether students were being sexually molested by Chavez.
Following a hearing on defendants’ motion to dismiss, and upon invitation of the court, the plaintiffs requested leave to file an amended complaint with respect to defendants Hayes and Fraissenet. The court granted the motion, and the amended complaint was filed. It contained additional allegations in support of showing knowledge of Hayes and Fraissenet, including that a parent had complained to a previous principal of the high school that Chavez had made sexual comments to girls at the school, that Chavez was removed from his position as a school bus driver because of inappropriate behavior with a preteen female student, and that Chavez was transferred to the high school after he had unhooked brassieres of junior high school girls.
We believe these allegations are insufficient to meet the first requirement of Gates. Chavez was employed by the school district for nineteen years. The plaintiffs allege four incidents and other rumors, none of which we believe demonstrates the requisite pattern of behavior necessary to support imposing liability. Compare Thelma D. ex rel. Delores A. v. Board of Educ., 934 F.2d 929, 933 (8th Cir.1991) (“[F]ive complaints scattered over sixteen years cannot, as a matter of law, be said to comprise a persistent and widespread pattern of unconstitutional misconduct”) and Jane Doe “A” ex rel. Jane Doe “B” v. Special Sch. Dist., 901 F.2d 642, 646 (8th Cir.1990) (even though various defendants were notified of isolated incidents occurring over a two-year period, no pattern of behavior was shown) with Doe v. Taylor Independent Sch. Dist., 15 F.Sd 443, 446, 456-57 (5th Cir.) (en banc) (“It was no secret within the school community that [the teacher] behaved inappropriately toward a number of young female students;” defendant principal had received complaints about specific inappropriate sexual behavior on the part of the teacher toward specific students and had previously cautioned teacher about specific acts; these complaints served as “a clear signal” of the sexual relationship), cert. denied, — U.S. -, 115 S.Ct. 70, 130 L.Ed.2d 25 (1994).
The plaintiffs presented no allegations, aside from one nonspecific statement by Fraissenet, that either Fraissenet or Hayes actually knew of the above incidents. Their argument that the defendants had constructive knowledge of these incidents is equally unavailing. “Imputation of constructive knowledge requires a showing that the underlying unconstitutional misconduct was ‘so widespread or flagrant that in the proper exercise of its official responsibilities the governing body should have known of [it].”’ Thelma D., 934 F.2d at 933 (quoting Spell v. McDaniel, 824 F.2d 1380, 1387 (4th Cir.1987), cert. denied, 484 U.S. 1027, 108 S.Ct. 752, 98 L.Ed.2d 765 (1988)). The plaintiffs have not made such a showing, and therefore, the district court properly dismissed the complaint against defendants Fraissenet and Hayes.
II.
The district court also dismissed the plaintiffs’ complaint against Chavez, holding he did not act “under color of state law” because his conduct was “so removed from his role as a custodian that [it] lack[ed] the color of law *492-necessary for a fair attribution of his acts to the governmental entity, as required under Section 1983 claims.”3
A.
Section 1983 created a federal cause of aetion for damages to vindicate alleged violations of federal law committed by individuals acting “under color of state law.” 42 TJ.S.C. § 1983; see also Wyatt v. Cole, 504 U.S. 158, 161, 112 S.Ct. 1827, 1830, 118 L.Ed.2d 504 (1992) (“[T]he purpose of § 1988 is to deter state actors from using the badge of their authority to deprive individuals of their federally guaranteed rights and to provide relief to victims if such deterrence fails.”); Owen v. City of Independence, 445 U.S. 622, 650, 100 S.Ct. 1398, 1415, 63 L.Ed.2d 673 (1980) (§ 1983 was designed “to provide protection to those persons wronged by the ‘[m]isuse of power’”). The statute “creates no substantive civil rights, only a procedural mechanism for enforcing them.” Wilson v. Meeks, 52 F.3d 1547, 1552 (10th Cir.1995). Therefore, “the only proper defendants in a Section 1983 claim are those who ‘represent [the state] in some capacity, whether they act in accordance with their authority or misuse it.’ ” Gallagher v. “Neil Young Freedom Concert”, 49 F.3d 1442, 1447 (10th Cir.1995) (quoting National Collegiate Athletic Ass’n v. Tarkanian, 488 U.S. 179, 191, 109 S.Ct. 454, 461-62, 102 L.Ed.2d 469 (1988)).
The “under color of state law” requirement is “a jurisdictional requisite for a § 1983 aetion,” Polk County v. Dodson, 454 U.S. 312, 315, 102 S.Ct. 445, 448, 70 L.Ed.2d 509 (1981), which, like its state action counterpart, furthers the fundamental goals of ‘“preserving] an area of individual freedom by limiting the reach of federal law and federal judicial power ... [and] avoiding] imposing on the State, its agencies or officials, responsibility for conduct for which they cannot fairly be blamed.’ ” Gallagher, 49 F.3d at 1447 (quoting Lugar v. Edmondson Oil Co., 457 U.S. 922, 936, 102 S.Ct. 2744, 2753, 73 L.Ed.2d 482 (1982)).4 Thus, private conduct that is not “fairly attributable” to the State is simply not actionable under § 1983, Rendell-Baker v. Kohn, 457 U.S. 830, 838, 102 S.Ct. 2764, 2769-70, 73 L.Ed.2d 418 (1982); see also D.T. ex rel. M.T. v. Independent School Dist. No. 16, 894 F.2d 1176, 1186 (10th Cir.), cert. denied, 498 U.S. 879, 111 S.Ct. 213, 112 L.Ed.2d 172 (1990), “however discriminatory or wrongful” the conduct is. See Shelley v. Kraemer, 334 U.S. 1, 13, 68 S.Ct. 836, 842, 92 L.Ed. 1161 (1948) (interpreting the “state action” requirement of the Fourteenth Amendment).5 But while the dichotomy between private conduct and governmental conduct is “well established and easily stated,” it “frequently admits of no easy answer.” Jackson v. Metropolitan Edison Co., 419 U.S. 345, 349-50, 95 S.Ct. 449, 453, 42 L.Ed.2d 477 (1974). Nonetheless, we can discern some parameters from existing law.
“The traditional definition of acting under color of state law requires that the defendant in a § 1983 action have exercised power ‘possessed by virtue of state law and made possible only because the wrongdoer is *493clothed with the authority of state law.’ ” West, 487 U.S. at 49, 108 S.Ct. at 2255 (quoting United States v. Classic, 313 U.S. 299, 326, 61 S.Ct. 1031, 1043, 85 L.Ed. 1368 (1941)). The authority with which the defendant is allegedly “clothed” may be either actual or apparent. See Pitchell v. Callan, 13 F.3d 545, 548 (2d Cir.1994); cf. Griffin v. Maryland, 378 U.S. 130, 135, 84 S.Ct. 1770, 1772-73,12 L.Ed.2d 754 (1964) (private security guard who wore a sheriffs badge and identified himself as a deputy sheriff “purported to exercise the authority of a deputy sheriff,” and was therefore a state actor for purposes of the equal protection clause of the Fourteenth Amendment).
In the public employment context, the Supreme Court has noted “state employment is generally sufficient to render the defendant a state actor.” Lugar, 457 U.S. at 935-36 n. 18, 102 S.Ct. at 2752-53 n. 18. But at the same time, it is “well settled that an otherwise private tort is not committed under color of law simply because the tortfeasor is an employee of the state.” Mark v. Borough of Hatboro, 51 F.3d 1137, 1150 (3d Cir.1995). While these statements might appear inconsistent on their face, we believe they can be reconciled.
Lugar can be understood as a recognition that an individual employed by the state who violates another individual’s federal rights will “generally” (i.e., in most cases), do so by virtue of the authority vested in them under state law. See Lugar, 457 U.S. at 935-36 n. 18, 102 S.Ct. at 2752-53 n. 18. Understood in this light, it is not difficult to understand that many tortious acts committed by state employees will occur in the performance of the employee’s official duties, and regardless of whether the employee “hew[s] to the line of their authority or overstep[s] it.” Screws v. United States, 325 U.S. 91, 111, 65 S.Ct. 1031, 1040, 89 L.Ed. 1495 (1945) (plurality opinion of Douglas, J.), that conduct will constitute action “under color of state law.” West, 487 U.S. at 50, 108 S.Ct. at 2256.
In Mark, however, the Third Circuit recognized, and we believe correctly so, that this “general” rule must give way because there are some circumstances where a tort by a state employee simply may not have been committed on account of the authority vested in the employee by the state. Under those circumstances, that “otherwise private tort” cannot automatically amount to action “under color of state law” so- as to support a § 1983 claim. For example, in Mark, the Third Circuit rejected the argument that a volunteer firefighter’s act of committing arson constituted action “under color of state law,” concluding the arsonist “acted in a purely private capacity when he committed the arson.” See Mark, 51 F.3d at 1150. Thus, the correlation between the fact that a tort was committed by an individual employed by the state does not, ipso facto, warrant attributing all of the employee’s actions to the state. See, e.g., Screws, 325 U.S. at 111, 65 S.Ct. at 1040 (“[U]nder ‘color’ of law means under ‘pretense’ of law.”). To do so would, for all practical purposes, overlook the important distinction between private and governmental conduct. Furthermore, such an interpretation would impermissibly' undermine the policies behind that well-established dichotomy by failing to recognize the existence of a zone of conduct beyond the scope of the federal judicial power6 and by improperly imposing liability on the state for conduct for which it cannot be fairly blamed. See Gallagher, 49 F.3d at 1447.. We decline to interpret the “under color of state law” requirement of § 1983 in such a manner.
As we have stated, before conduct may be fairly attributed to the state because it constitutes action “under color of state law,” there must be “a real nexus” between the employee’s use or misuse of their authority as a public employee, and the violation allegedly committed by the defendant. See D.T., 894 F.2d at 1188; Barna, 42 F.3d at 817 (collecting cases); Pitchell, 13 F.3d at 548 (collecting cases). Such an interpretation is entirely consistent with the Supreme Court’s pronouncement that § 1983 is only intended to deter state officials from “using the badge of their authority” to deny citizens their federally protected rights. Wyatt, 504 *494U.S. at 161, 112 S.Ct. at 1830. Therefore, it is the plaintiffs burden to plead, and ultimately establish, the existence of “a real nexus” between the defendant’s conduct and the defendant’s “badge” of state authority in order to demonstrate action was taken “under color of state law.”
B.
Applying these principles to this case, we agree with the district court that the plaintiffs’ complaint is deficient on the question of whether Chavez acted “under color of state law.” The well-pleaded allegations in the complaint, even when taken as true, are insufficient to demonstrate Chavez possessed state authority (either actual or apparent), and if he did possess such authority, that he exercised it-in relation to his molestation of Bridget Jojola.7 The complaint is devoid of any allegation that Chavez enticed Bridget into the classroom through the use or misuse of any state authority he may have possessed.
Furthermore, when asked about this issue by the district court during argument on the motion to dismiss, the following colloquy occurred between the court and plaintiffs’ counsel:
THE COURT: Let’s talk about the individual capacity claims against these people who you say were acting under color of law. Let’s first address Jimmy Chavez. ...
In this intentional sexual act that he is accused of, how is that under color of law? Can you tell me how that would happen?
[PLAINTIFFS’ COUNSEL]: Your Honor, I can’t answer you.
• THE COURT: All right. There’s no question, however, that he has committed a tort. But how is it under color of law? And you and I have, I think, agreed that we can’t conceive of a way to do that.
Although plaintiffs’ counsel was unable to articulate to the district court how Chavez’s conduct could be fairly attributed to the state, counsel attempts to overcome this deficiency on appeal by making arguments that extend beyond the allegations in the complaint. It is well-established, however, that in determining whether to grant a motion to dismiss, the district court, and consequently this court, are limited to assessing the legal sufficiency of the allegations contained within the four corners of the complaint. See, e.g., Doyle v. Oklahoma Bar Ass’n, 998 F.2d 1559, 1566 (10th Cir.1993) (in reviewing an order granting a motion to dismiss, court of appeals “confin[es] [its] review to the allegations of the complaint”). Therefore, extraneous arguments in an appellate brief may not be relied upon to circumvent pleading defects.8
Because the complaint fails to allege any facts purporting to establish the requisite nexus between Chavez’s tortious conduct and the exercise of state authority, the complaint fails to state a claim against Chavez under § 1983. While Chavez’s conduct is not to be condoned or sanctioned, the only question before us is whether that conduct may be redressed as a violation of federal law. As we have indicated, § 1988 is not a panacea that is available to remedy all types of tortious behavior, and unless Chavez’s conduct can be fairly attributed to the state, the remedy provided under § 1983 will not be available. We agree with the district court that the allegations in the complaint relative to the constitutional claims against Chavez do not overcome the barrier differentiating purely private conduct from conduct attributable to the government.
*495CONCLUSION
We AFFIRM the district court’s order dismissing the plaintiffs’ § 1983 claims against defendants Hayes, Fraissenet and Chavez.9
. While the Gates court identified three other elements plaintiffs must prove, we need not discuss these factors as we resolve the issue solely on the factor set forth above.
. While plaintiffs also alleged Fraissenet and Hayes had a duty to protect Bridget Jojola from Chavez, this argument is without merit. See Graham v. Independent Sch. Dist. No. I-89, 22 F.3d 991, 994 (10th Cir.1994) ("compulsory school attendance laws do not spawn an affirmative duty to protect under the Fourteenth Amendment"); Maldonado v. Josey, 975 F.2d 727, 731 (10th Cir.1992) (compulsory attendance laws do not restrain a student's liberty such as to give rise to an affirmative duty to protect the student), cert. denied, -U.S. -, 113 S.Ct. 1266, 122 L.Ed.2d 662 (1993).
. The defendants argue the plaintiffs may not raise this issue on appeal because they did not raise it before the district court. The plaintiffs' complaint alleged Chavez "was acting under col- or of law” at the time he molested Bridget Jojola, and the district court dismissed the plaintiffs’ claims against Chavez on that ground. While inartfully argued to the district court, we believe the plaintiffs did properly raise this issue for the district court's consideration.
. Neither the civil rights statutes nor the Fourteenth Amendment are a license to the federal judiciary to displace state law through the creation of a body of general federal tort law. See Paul v. Davis, 424 U.S. 693, 701, 96 S.Ct. 1155, 1160-61, 47 L.Ed.2d 405 (1976) (Fourteenth Amendment); Griffin v. Breckenridge, 403 U.S. 88, 101-02, 91 S.Ct. 1790, 1797-98, 29 L.Ed.2d 338 (1971) (civil rights statute).
."[I]n § 1983 actions the statutory requirement of action 'under color of' state law is just as broad as the Fourteenth Amendment's 'state action' requirement.” Hafer v. Melo, 502 U.S. 21, 28, 112 S.Ct. 358, 363, 116 L.Ed.2d 301 (1991) (quoting Lugar, 457 U.S. at 929, 102 S.Ct. at 2749); see also West v. Atkins, 487 U.S. 42, 48, 108 S.Ct. 2250, 2254-55, 101 L.Ed.2d 40 (1988) (citing cases). Therefore, we look to decisional law interpreting the "state action” requirement for guidance in deciding whether certain conduct was taken "under color of state law” for purposes of § 1983.
. “[Plurely private acts which are not furthered by any actual or purported state authority are not acts under color of state law.” Barna v. City of Perth Amboy, 42 F.3d 809, 816 (3d Cir.1994).
. The only allegations in the complaint relevant to Chavez’s conduct are "Bridget was accosted by Defendant Chavez,” and "[d]efendant Chavez forcibly lead [sic] Bridget into- a vacant and dark classroom and thereafter unlawfully touched and applied force to her person, including to the intimate parts of her body, committing the act of criminal sexual penetration.”
. In any event, even if these arguments had been set forth in the complaint, it would not alter our conclusion because those arguments are conclu-sory statements, and not well-pleaded facts. See, e.g., Swanson v. Bixler, 750 F.2d 810, 813 (10th Cir.1984) (in reviewing a motion to dismiss, "[a]ll well-pleaded facts, as distinguished from conclusory allegations, must be taken as true.”); accord Hall v. Bellmon, 935 F.2d 1106, 1110 (10th Cir.1991).
. The plaintiffs have not appealed the portion of the district court's order declining to exercise supplemental jurisdiction over their state law ' claims. See 28 U.S.C. § 1367(c). Therefore, that ruling stands as the law of the case.