As a natural variant of the many decycling notions studied in graphs, we consider the problem to decide whether a given graph G has a matching M such that G−M is a forest. We establish NP-completeness of this problem for 2-connected planar subcubic graphs, and describe polynomial time algorithms that also determine such a matching if it exists for graphs that are claw- and paw-free, P5-free, chordal, and C4-free distance hereditary.
CITATION STYLE
Lima, C. V. G. C., Rautenbach, D., Souza, U. S., & Szwarcfiter, J. L. (2017). Decycling with a matching. Information Processing Letters, 124, 26–29. https://doi.org/10.1016/j.ipl.2017.04.003
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