On Color Critical Graphs of Star Coloring

05/29/2023

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by   Harshit Kumar Choudhary, et al.

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A star coloring of a graph G is a proper vertex-coloring such that no path on four vertices is 2-colored. The minimum number of colors required to obtain a star coloring of a graph G is called star chromatic number and it is denoted by χ_s(G). A graph G is called k-critical if χ_s(G)=k and χ_s(G -e) < χ_s(G) for every edge e ∈ E(G). In this paper, we give a characterization of 3-critical, (n-1)-critical and (n-2)-critical graphs with respect to star coloring, where n denotes the number of vertices of G. We also give upper and lower bounds on the minimum number of edges in (n-1)-critical and (n-2)-critical graphs.