Abstract
For an integer r > 0 , a conditional ( k , r ) - coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent to vertices with at least r different colors. The smallest integer k for which a graph G has a conditional ( k , r ) -coloring is the rth order conditional chromatic number χ r ( G ) . In this paper, the behavior and bounds of conditional chromatic number of a graph G are investigated.
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