Star Coloring of Certain Graph Classes
Graphs and Combinatorics
A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on four vertices (not necessarily induced) is bi-colored. The star chromatic number of G, denoted by χs(G) , is the minimum number of colors needed to star color G. Similar to the notion of χ-boundedness in graphs, we say that a hereditary class of graphs G is χs-bounded if, for some integer valued function f, χs(G) ≤ f(ω(G)) for every G∈ G, where ω(G) is the maximum number of vertices that are pairwise adjacent in G. We show that some classes of perfect graphs, some classes of (P5, C4)-free graphs, and some classes of K1 , 3-free graphs are χs-bounded. We also give examples in most of the cases to show that the bounds are tight.
Karthick, T., "Star Coloring of Certain Graph Classes" (2018). Journal Articles. 1606.