On the vertex arboricity of graphs with prescribed size
نویسندگان
چکیده
ON THE VERTEX ARBORICITY OF GRAPHS WITH PRESCRIBED SIZE Nirmala Achuthan, N.R. Achuthan and L. Caccetta School of Mathematics and Statistics Curtin University of Technology G.P.O. Box U1987 PERTH WA 6845 Let ~(n) denote the class of simple graphs of order n and ~(n,m) the subclass of graphs with size m. G denotes the complement of a graph G. For a graph G, the vertex arboricity p(G), is the minimum number of colours needed to colour the vertices of G such that every colour class is acyclic. In this paper we determine the range for the size of a graph G E ~(n) with prescribed arboricity. We also characterize the extremal graphs. Further, we establish sharp bounds for the sum p(G) + p( G) and the product p(G).p(G), where G ranges over ~(n,m). We determine the class of graphs G for which p(G).p(G) attains the minimum value.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 1999