Decycling a Graph by the Removal of a Matching: Characterizations for Special Classes.
A graph $G$ is matching-decyclable if it has a matching $M$ such that $G-M$ is acyclic. Deciding whether $G$ is matching-decyclable is an NP-complete problem even if $G$ is 2-connected, planar, and subcubic. In this work we present characterizations of matching-decyclability in the following classes: chordal graphs, split graphs, distance-hereditary graphs, cographs, and Hamiltonian subcubic graphs. All the characterizations lead to simple $O(n)$-time recognition algorithms.
Publisher URL: http://arxiv.org/abs/1707.02473
DOI: arXiv:1707.02473v3
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