TRIANGLES IN 2-FACTORIZATIONS

The triangle-spectrum for 2-factorizations of the complete graph K-v i s the set of all numbers delta such that there exists a 2-factorizatio n of K-v in which the total number of triangles equals delta. By apply ing mainly design-theoretic methods, we determine the triangle spectru m for all v = 1 or 3(mod 6), v greater than or equal to 43, as well as for v = 7, 9, 13, 15, 21, and 27. For orders v = 19, 25, 31, 33, 37, 39, we leave only a total of 11 values undecided. To determine the tri angle-spectrum for v = 5 (mod 6) remains an Open problem. (C) 1997 Joh n Wiley & Sons, Inc.