2012/08/04 by Zhidan Yan, Wei Wang, Yan, Zhidan +1 · 1 citation
Computer Science · Mathematics · #05C15 #Advanced Graph Theory Research #FOS: Mathematics #Graph Labeling and Dimension Problems #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR #msc:05C15
paper · pdf · doi:10.48550/arxiv.1208.0918
The Primary Category is not correct. We would like to resubmit it
openalex publication_date 2012/08/04 · arxiv created 2013/07/09 · arxiv updated 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most 1. The equitable chromatic threshold of a graph G, denoted by χ_=^*(G), is the minimum k such that G is equitably k^′-colorable for all k^′ ≥ k. Let G× H denote the direct product of graphs G and H. For n≥ m≥ 2 we prove that χ_=^*(Km × Kn) equals \lceil(mn)/(m+1)\rceil if n≡ 2,...,m (\textupmod m+1), and equals m\lceil(n)/(s^⋆)\rceil if n≡ 0,1 (\textupmod m+1), where s^⋆ is the minimum positive integer such that s^⋆ \nmid n and s^⋆≥ m+2.