B-chromatic Number of Cacti
نویسندگان
چکیده
A b-colouring of a graph G is a proper colouring of G such that each colour contains a vertex that is adjacent to all other colours and the b-chromatic number χb(G) is the maximum number of colours used in a b-colouring of G. If m(G) is the largest integer k such that G has at least k vertices with degree at least k − 1, then we know that χb(G) ≤ m(G). Irving and Manlove [1] prove that, if T is a tree, then the b-chromatic number of T is at least m(T ) − 1. In this paper, we prove that, if G is a connected cactus and m(G) ≥ 7, then the b-chromatic number of G is at least m(G) − 1.
منابع مشابه
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 35 شماره
صفحات -
تاریخ انتشار 2009