On Alspach's Conjecture

Publisher This chapter describes on Alspach's conjecture. The chapter shows that if all cycles are of length 3, 4 or 6, and if n is odd and 3a + 4b + 6c = n(n - 1)/2, or if n is even and 3a + 4b + 6c = n(n - 2)/2, then G = aC3 + bC4 + cC6 where G = Kn if n is odd and G = Kn - F if n is even. Some theorems and their proofs are also described in the chapter.