Equitable colorings of Kronecker products of graphs

Wu-Hsiung Lin, Gerard J. Chang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


For a positive integer k, a graph G is equitably k-colorable if there is a mapping f:V(G)→1,2,⋯,k such that f(x)≠f(y) whenever xy∈E(G) and ||f-1(i)|-|f-1(j)||≤1 for 1≤i<j≤k. The equitable chromatic number of a graph G, denoted by χ=(G), is the minimum k such that G is equitably k-colorable. The equitable chromatic threshold of a graph G, denoted by χ=*(G), is the minimum t such that G is equitably k-colorable for k<t. The current paper studies equitable chromatic numbers of Kronecker products of graphs. In particular, we give exact values or upper bounds on χ=(G×H) and χ=*(G×H) when G and H are complete graphs, bipartite graphs, paths or cycles.

Original languageEnglish
Pages (from-to)1816-1826
Number of pages11
JournalDiscrete Applied Mathematics
Issue number16
StatePublished - 28 Aug 2010


  • Equitable chromatic number
  • Equitable chromatic threshold
  • Equitable coloring
  • Kronecker product

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