Refining the Graph Density Condition for the Existence of Almost K-factors

Alon and Yuster [4] have proven that if a fixed graph K on g vertices is (h + 1)-colorable, then any graph G with n vertices and minimum degree at least h h+1 n contains at least (1 - )n g vertex disjoint copies of K, provided n > N( ). It is shown here that the required minimum degree of G for this result to follow is closer to h-1 h n, provided K has a proper (h + 1)-coloring in which some of the colors occur rarely. A conjecture regarding the best possible result of this type is suggested.

• Type: Journal
• Year: 1999
• Where: ARSCOM
• Authors: Noga Alon, Eldar Fischer
• Keywords: Alon, ARSCOM 1999, Fixed Graph, Minimum Degree