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 NPcomplete 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.

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