In this paper we prove the following conjecture of Alon and Yuster. Let H be a graph with h vertices and chromatic number k. There exist constants c(H) and n0(H) such that if n ≥ n0(H) and G is a graph with hn vertices and minimum degree at least (1 - 1/k)hn + c(H), then G contains an H-factor. In fact, we show that if H has a k-coloring with color-class sizes h1 ≤ h2 ≤ ⋯ ≤ hk, then the conjecture is true with c(H)=hk+hk-1 - 1.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics