Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials
Combinatorics
2009-09-30 v1
Abstract
In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define -barrier sets. Our definition of a -barrier set is slightly different from that of a barrier set. However we show that -barrier sets and barrier sets have similar properties. In particular, we prove a generalized Berge's Formula and give a characterization for the set of all -special vertices in a graph.
Keywords
Cite
@article{arxiv.0909.5249,
title = {Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials},
author = {Cheng Yeaw Ku and Kok Bin Wong},
journal= {arXiv preprint arXiv:0909.5249},
year = {2009}
}