The matching number of tree and bipartite degree sequences
Abstract
We study the possible values of the matching number among all trees with a given degree sequence as well as all bipartite graphs with a given bipartite degree sequence. For tree degree sequences, we obtain closed formulas for the possible values. For bipartite degree sequences, we show the existence of realizations with a restricted structure, which allows to derive an analogue of the Gale-Ryser Theorem characterizing bipartite degree sequences. More precisely, we show that a bipartite degree sequence has a realization with a certain matching number if and only if a cubic number of inequalities similar to those in the Gale-Ryser Theorem are satisfied. For tree degree sequences as well as for bipartite degree sequences, the possible values of the matching number form intervals.
Keywords
Cite
@article{arxiv.1808.09650,
title = {The matching number of tree and bipartite degree sequences},
author = {F. Bock and D. Rautenbach},
journal= {arXiv preprint arXiv:1808.09650},
year = {2018}
}