Spectral characterization of matchings in graphs
Combinatorics
2016-02-12 v1
Abstract
A spectral characterization of the matching number (the size of a maximum matching) of a graph is given. More precisely, it is shown that the graphs G of order n whose matching number is k are precisely those graphs with the maximum skew rank 2k such that for any given set of k distinct nonzero purely imaginary numbers there is a real skew-symmetric matrix A with graph G whose spectrum consists of the given k numbers, their conjugate pairs, and n-2k zeros.
Keywords
Cite
@article{arxiv.1602.03590,
title = {Spectral characterization of matchings in graphs},
author = {Keivan Hassani Monfared and Sudipta Mallik},
journal= {arXiv preprint arXiv:1602.03590},
year = {2016}
}
Comments
16 pages, accepted in Linear Algebra and its Applications (2016)