Vertex arboricity and maximum degree
نویسندگان
چکیده
The vertex arboricity of graph G is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. We prove results such as this: if a connected graph G is neither a cycle nor a clique, then there is a coloring of V(G/ with at most [-A(G)/2 ~ colors, such that each color class induces a forest and one of those induced forests is a maximum induced forest in G. This improves prior results of Brooks [ 19411, Kronk and Mitchem (1974/75), and LovS.sz (1966), and it is analogus to a result of Catlin (1976. 1979) on the chromatic number that improves Brooks' theorem. Kevwords. Arboricity: Vertex arboricity; Chromatic number
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 141 شماره
صفحات -
تاریخ انتشار 1995