An Ore-type theorem on equitable coloring

A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this note, we prove that if G is a graph such that for each edge xy E(G), the sum d(x) + d(y) of the degrees of its ends is at most 2r + 1 then G has an equitable coloring with r + 1 colors. This extends the Hajnal-Szemer

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Hal A. Kierstead, Alexandr V. Kostochka
• Keywords: Color Classes, Hajnal-Szemer´edi Theorem, JCT 2008, Proper Vertex