Injective colorings of sparse graphs

Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; similarly, if Mad(G) < 42 19 , then i(G) . Suppose that G is a planar graph with girth g(G) and 4. We prove that if g(G) 9, then i(G) + 1; similarly, if g(G) 13, then i(G) = .

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Daniel W. Cranston, Seog-Jin Kim, Gexin Yu
• Keywords: Chromatic, DM 2010, Injective Chromatic Number, Maximum Average Degree