A lower bound on the acyclic matching number of subcubic graphs

M. Fürst; D. Rautenbach

A lower bound on the acyclic matching number of subcubic graphs

Combinatorics 2017-10-30 v1

Authors: M. Fürst , D. Rautenbach

Abstract

The acyclic matching number of a graph $G$ is the largest size of an acyclic matching in $G$ , that is, a matching $M$ in $G$ such that the subgraph of $G$ induced by the vertices incident to an edge in $M$ is a forest. We show that the acyclic matching number of a connected subcubic graph $G$ with $m$ edges is at least $m/6$ except for two small exceptions.

Keywords

acyclic matching number subcubic graphs matching forest graph theory lower bound

Cite

@article{arxiv.1710.10076,
  title  = {A lower bound on the acyclic matching number of subcubic graphs},
  author = {M. Fürst and D. Rautenbach},
  journal= {arXiv preprint arXiv:1710.10076},
  year   = {2017}
}

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