On the Core of a Unicyclic Graph
Discrete Mathematics
2011-02-24 v1 Combinatorics
Abstract
A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G) is the size of a maximum matching in G. A connected graph having only one cycle, say C, is a unicyclic graph. In this paper we prove that if G is a unicyclic graph of order n and n-1 = alpha(G) + mu(G), then core(G) coincides with the union of cores of all trees in G-C.
Cite
@article{arxiv.1102.4727,
title = {On the Core of a Unicyclic Graph},
author = {Vadim E. Levit and Eugen Mandrescu},
journal= {arXiv preprint arXiv:1102.4727},
year = {2011}
}
Comments
8 pages, 5 figures