Injective colorings of graphs with low average degree

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 4 and mad(G) < 14 5 , then i(G) + 2. When = 3, we show that mad(G) < 36 13 implies i(G) 5. In contrast, we give a graph G with = 3, mad(G) = 36 13 , and i(G) = 6.

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