This action to desegregate the public schools of Tulsa, Oklahoma was brought by the United States in July 1968 under section 407(a) of the 1964 Civil Rights Act, 42 U.S.C. Sec. 2000c-6. The district court dismissed the complaint after a full trial on the merits and appeal was taken to this court. We concluded from the record in that appeal that the policies and practices of the defendant school district constituted a subtle but effective system of state-imposed and state-preserved racial segregation. We therefore reversed and remanded the cause to the district court with orders that the defendant school district begin immediately to effect the disestablishment of the segregated school system in Tulsa. Our opinion in that appeal, reported 429 F.2d 1253, contains a description of the factual context in which this litigation arose, detailing the racial composition of specific schools in the district and the segregated conditions in the district as a whole. It is not necessary to repeat those facts here, and we incorporate by reference the factual description contained in our prior opinion.

On remand to the district court, the United States and the school district reached agreement on all issues except student assignment in the elementary schools. Under the agreement, faculty members are to be assigned to achieve a ratio of black to white teachers in each school equal to the ratio in the system as a whole. The transfer policies have been redesigned to eliminate transfers that promote segregation. A majority to minority transfer policy has been established that provides transferees free transportation where necessary and admission to closest schools on a priority basis. The agreement also provides that all future school construction will be done in a manner calculated affirmatively to promote the maintenance of a unitary school system free from racial discrimination. The school district agrees to file annual reports with the court and opposing counsel giving information as to racial composition of students and faculty in each school, a list of transfers including the race of transferees and reasons for transfer, and plans for school construction.

The question of student assignment on the secondary level was resolved by the adoption of plans of desegregation for junior and senior high schools. The desegregation plan for junior high schools closed two schools, all-black Carver Junior High and predominately white Lowell Junior High. The attendance boundaries of the remaining schools were redrawn so that no junior high school in the district had a student enrollment of more than 33 percent black. The desegregation plan for senior high schools created a Metro Learning Center at formerly all-black Washington High School to operate in conjunction with the regular high school until the 1973-74 school year when Mason High School will be completed. At that time the physical facilities at Washington High will be used entirely for the Metro Learning Center enrolling 800 to 1,000 students on an integrated basis. The black student enrollment in the remaining high schools will be from 7 to 22 percent.

On the issue of desegregation of the elementary schools the parties were unable to agree. The district court held an evidentiary hearing on the matter and ruled that five of the nine black elementary schools were de facto segregated, their segregated status resulting not by discriminatory state action but by population movements. The court concluded that it was judicially unnecessary to order change in the five de facto schools because no wrong had been committed by the state. The court ruled the four remaining schools to be de jure segregated and ordered the school district to desegregate them. The school district subsequently submitted a plan to which the United States agreed, fully desegregating each of the four schools.

The United States appeals from the portion of the judgment ruling that five of the elementary schools are de facto segregated. The intervening-appellants likewise disagree with the district court's finding with regard to the de facto schools. In addition, they ask this court to reverse the district court's judgment approving the plan for student assignment on the junior high and senior high school levels. They argue that the student assignment plan on the secondary level places a disproportionate share of the burden of desegregation on the black community.

The five elementary schools determined by the court to be de facto segregated are Burroughs (85.5% black), Emerson (91.3% black), Frost (99.4% black), Hawthorne (95.9% black), and Whitman (96.7% black). Three of the five schools, Burroughs, Emerson, and Whitman, were operating as all-white schools in all-white neighborhoods at the time of Brown v. Board of Education (Brown I), 347 U.S. 483, 74 S. Ct. 686, 98 L. Ed. 873 in 1954. Whitman opened as an all-white school in 1961. Frost opened in 1966 with one white student and 458 black students.

The story of the change in racial composition of the four formerly all-white schools is a familiar one. Changes in housing laws removing racial restrictions on residential property allowed blacks to move into the white neighborhoods surrounding the well-defined black areas to which they had formerly been restricted. This outward movement of blacks, combined with the familiar "white flight" has converted many white residential areas into all-black neighborhoods with a corresponding effect on the schools. Burroughs was built in 1925 and operated as an all-white school until 1957 when it enrolled its first black students; by 1962 Burroughs was all black. Emerson was built in 1913 and enrolled eleven black students for the first time in 1955 and by 1963 was 83% black. Hawthorne enrolled six black students in 1961 and was 87% black by 1967. Whitman opened as an all-white school in 1961, enrolled four black students the following year, and by 1970 it had become 95% black.

Frost is the only one of the five de facto segregated schools which has been predominately black from its beginning. Before the school was constructed, surveys of the projected attendance area indicated enrollment would be approximately 70% black and 30% white. In the interim between the acquisition of the site and the opening of the school, the racial composition of the attendance area changed and the school opened with an essentially all-black enrollment.

In reviewing the findings of the district court with regard to these five schools this court is bound by the standard of review required by Rule 52, Fed. R.Civ.P. Unless we are satisfied that the trial court's findings are clearly erroneous we must defer to them. In referring to the five schools in question the district court found that "[t]hese schools since Brown I have not been subjected to state imposed segregation, either by law or school board policy. They are now predominately black solely because of blacks moving into their respective neighborhoods." The findings are amply supported by evidence in the record and we conclude that they are not clearly erroneous.

The United States contends, however, that the court's findings lack specificity and do not present an adequate basis for review by this court. See Deal v. Cincinnati Board of Education, 6 Cir., 369 F.2d 55. We do not agree. Because of the complexities present and pertaining to these individual schools, the trial court was required, so says the United States, to evaluate in its findings such evidence as might have dispositive impact on whether these schools were in de facto segregation without state fault. Such factors as transfer policy, zoning decisions, faculty assignments and site selections1 are designated as necessary subjects for specific findings. We do not agree that it was necessary for the trial court to set up a series of straw men. The judicial process does not require a trial court to detail, set out, and evaluate evidence simply to supply proof of subjective recognition of its potential impact but negation of its impact on the ultimate fact. However we give brief consideration to appellant's affirmative arguments directed to claims of error in the court's determination that the subject schools were constitutionally de facto.

The appellant and intervenors point to this court's notation in United States v. Board of Education, Ind. Sch. Dist. No. 1, Tulsa County, Okla., 429 F.2d 1253, that the Tulsa School Board had maintained a minority to majority transfer policy from 1962 to 1965 which served as an efficient tool to maintain segregation. They argue that the transfer policy constituted "state action" and therefore the district court's finding of de facto segregation must be reversed. There is no evidence in the record, however, indicating that the minority to majority transfer policy substantially affected the racial composition of the attendance zones of the schools in question. Indeed, it must be recognized that such a transfer policy does not go into effect until the school is already majority black.

The law of this circuit has been consistently stated by the court to be that neighborhood school plans, when impartially maintained and administered, do not violate constitutional rights even though the result of such plans is racial imbalance. Keyes v. School District No. 1, Denver, Colo., 10 Cir., 455 F.2d 990, cert. granted, 404 U.S. 1036, 92 S. Ct. 707, 30 L. Ed. 2d 728; United States v. Board of Educ., Ind. Sch. Dist. No. 1, Tulsa, Okl., 10 Cir., 429 F.2d 1253; Board of Educ. of Oklahoma City Pub. Schools v. Dowell, 10 Cir., 375 F.2d 158, cert. denied, 387 U.S. 931, 87 S. Ct. 2054, 18 L. Ed. 2d 993. The mere existence of one-race schools, whether black or white, does not establish a constitutional violation. Neither black nor white children have a constitutional right to attend public schools with children of the other race. Downs v. Board of Educ. of Kansas City, 10 Cir., 336 F.2d 988, cert. denied, 380 U.S. 914, 85 S. Ct. 898, 13 L. Ed. 2d 800. A constitutional violation exists only when it can be shown that the existence of the one-race school and its attendance by children of that race is due to some form of discriminatory state action, however subtle that may be. Without a showing of a constitutional violation on the part of school authorities, equity does not require a federal court to effect changes in the racial composition of public schools. Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 91 S. Ct. 1267, 28 L. Ed. 2d 554; Keyes v. School District No. 1, Denver, Colo., 10 Cir., 445 F.2d 990, cert. granted, 404 U.S. 1036, 92 S. Ct. 707, 30 L. Ed. 2d 728. Having found an absence of discriminatory state action with regard to the racial composition of the five schools in question, the district court correctly recognized that to order a desegregation plan for those schools would be beyond the equity power of the federal courts.

The intervening-appellants challenge the district court's approval of the desegregation plan for the junior and senior high schools, claiming that the plan places a disproportionate share of the burden of desegregation on the black community. The record does not support this contention. The plan is also challenged because it does not desegregate all-black Washington High School until the completion of the new Mason High School in 1973. This element of the plan is alleged to violate the Supreme Court's mandate in Alexander v. Holmes County Bd. of Educ., 396 U.S. 19, 90 S. Ct. 29, 24 L. Ed. 2d 19, that plans must be implemented "at once" to desegregate the schools. We hasten to point out the Supreme Court has also stated that under appropriate circumstances some schools may remain one-race schools until new schools are built. Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 91 S. Ct. 1267, 28 L. Ed. 2d 554. The student assignment plan for secondary schools agreed to by the parties and approved by the district court is a good one. There is no universal plan for desegregation that will fit the problems of every school district. Neither is it possible to devise a plan that will please everyone. Desegregation plans must be formulated on a case-by-case basis, and preferably formulated and agreed to by the parties involved. Their validity should not depend on the whim or preferences of members of the federal judiciary. They must be judged by constitutional standards. If they accomplish the desired goal of creating a unified school system, and do so in non-discriminatory manner, we are constrained to approve them. United States v. Jefferson County Bd. of Educ., 5 Cir., 380 F.2d 385, cert. denied, Board of Ed. of City of Bessemer, v. United States, 389 U.S. 840, 88 S. Ct. 77, 19 L. Ed. 2d 104. The plan approved by the district court is constitutionally sound. The judgment of the district court is affirmed.