Equitable coloring of corona products of cubic graphs is harder than ordinary coloring

Hanna Furmanczyk, Marek Kubale

Abstract


A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by χ = (G). In this paper the problem of determinig χ =  for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas of cubic graphs is solvable in polynomial time, the problem of equitable coloring becomes NP-hard for these graphs. We provide polynomially solvable cases of coronas of cubic graphs and prove the NP-hardness in a general case. As a by-product we obtain a simple linear time algorithm for equitable coloring of such graphs which uses χ = (G) or χ = (G) + 1 colors. Our algorithm is best possible, unless P=NP. Consequently, cubical coronas seem to be the only known class of graphs for which equitable coloring is harder than ordinary coloring.


Keywords


Corona graph, cubic graph, equitable chromatic number, equitable graph coloring, NP-hardness, polynomial algorithm

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DOI: https://doi.org/10.26493/1855-3974.687.99b

ISSN: 1855-3974

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