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Injective chromatic number and chromatic number of the square of graphs
, 2009
"... The injective chromatic number of a graph G is the minimum number of colors needed in order to color vertices of G so that two vertices with a common neighbor receive distinct colors. We prove that the injective chromatic number of G is at least the half of the chromatic number of G2, the square of ..."
Abstract

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The injective chromatic number of a graph G is the minimum number of colors needed in order to color vertices of G so that two vertices with a common neighbor receive distinct colors. We prove that the injective chromatic number of G is at least the half of the chromatic number of G2, the square of G. This inequality is tight.