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Determination of the star valency of a graph

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Abstract

The star valency of a graph G is the minimum, over all star decompositions π, of the maximum number of elements in π incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either ⌈dmax-ave(G)/2⌉ or ⌈dmax-ave(G)/2⌉+1, and provide a polynomial time algorithm for determining the star valency of a graph.

Keywords

Graph
Star valency
Average degree
Orientation
Algorithm

Cited by (0)

1

Partially supported by NNSFC under Grant No. 19831080.

2

Partially supported by the National Security Agency under Grants MDA-904-96-1-0014 and MDA-904-01-1-0022.

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