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The even-girth of any graph G is the smallest length of any even cycle in G. For any two integers t,k with 0≤t≤k−2, we denote the maximum number of cycles of length k such that each pair of cycles intersect in exactly a unique path of length t by bt,k(G). This parameter is called the (t,k)-booksize of G. In this paper we obtain some upper bounds for the chromatic and coloring numbers of graphs in...
In this paper we discuss the existence of lower bounds for the chromatic number of graphs in terms of the average degree or the coloring number of graphs. We obtain a lower bound for the chromatic number of K1,t-free graphs in terms of the maximum degree and show that the bound is tight. For any tree T, we obtain a lower bound for the chromatic number of any K2,t-free and T-free graph in terms of...
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