Equitable colorings of Cartesian products of square of cycles and paths with complete bipartite graphs

Shasha Ma and Liancui Zuo ()
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Shasha Ma: Tianjin Normal University
Liancui Zuo: Tianjin Normal University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 3, No 5, 725-740

Abstract: Abstract A graph G is said to be equitably k-colorable if the vertex set of G can be divided into k independent sets for which any two sets differ in size at most one. The equitable chromatic number of G, $$\chi _{=}(G)$$ χ = ( G ) , is the minimum k for which G is equitably k-colorable. The equitable chromatic threshold of G, $$\chi _{=}^{*}(G)$$ χ = ∗ ( G ) , is the minimum k for which G is equitably $$k'$$ k ′ -colorable for all $$k'\ge k$$ k ′ ≥ k . In this paper, the exact values of $$\chi _{=}^{*}(G\Box H)$$ χ = ∗ ( G □ H ) and $$\chi _{=}(G\Box H)$$ χ = ( G □ H ) are obtained when G is the square of a cycle or a path and H is a complete bipartite graph.

Keywords: Equitable coloring; Equitable chromatic number; Equitable chromatic threshold; Cartesian product (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9895-5

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