Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials

Details Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials

2009-09-29

arxiv.org/abs/0909.5249v1

Mathematics

Combinatorics

Scientific paper

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 $\theta$-barrier sets. Our definition of a $\theta$-barrier set is slightly different from that of a barrier set. However we show that $\theta$-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 $\theta$-special vertices in a graph.

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