通过移除匹配来去环化图：某些图类中新的算法与结构方面
Decycling a graph by the removal of a matching: new algorithmic and structural aspects in some classes of graphs
AI总结：
本文研究通过移除匹配使图变为无环的问题，在哈密顿次立方图中证明NP完全性，并为弦图和距离遗传图提供线性时间识别算法。
摘要：
如果图$G$存在一个匹配$M$使得$G-M$是无环的，则称$G$为匹配可去环化图。判断$G$是否为匹配可去环化图是一个NP完全问题，即使$G$是2-连通、平面且次立方的。本文研究了以下图类中的匹配可去环化性：哈密顿次立方图、弦图和距离遗传图。在哈密顿次立方图中，我们证明即使恰好有两个度为2的顶点，判断匹配可去环化性仍是NP完全的。对于弦图和距离遗传图，我们给出了匹配可去环化性的刻画，从而得到$O(n)$时间的识别算法。
英文摘要：
A graph $G$ is {\em 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 results on matching-decyclability in the following classes: Hamiltonian subcubic graphs, chordal graphs, and distance-hereditary graphs. In Hamiltonian subcubic graphs we show that deciding matching-decyclability is NP-complete even if there are exactly two vertices of degree two. For chordal and distance-hereditary graphs, we present characterizations of matching-decyclability that lead to $O(n)$-time recognition algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
