论文标题
查找$ h $ free图中的匹配削减
Finding Matching Cuts in $H$-Free Graphs
论文作者
论文摘要
NP完整的问题匹配切割是确定图形是否具有匹配，这也是图形的边缘切割。我们证明，匹配剪切的新复杂性结果仅限于$ h $ free Graphs，即不包含一些固定图$ H $作为诱导子图的图形。我们还证明了两个最近研究的匹配切割变体的新复杂性结果，即$ h $ free图。第一个变体要求匹配切割必须可扩展到图表的完美匹配。第二个变体要求匹配切割是完美的匹配。特别是，我们证明存在一个小的常数$ r> 0 $，因此第一个变体对于$ p_r $ - free-free-free-free-free图。这解决了花束和皮克洛的问题（Arxiv，2020年）。对于所有三个问题，我们将其计算复杂性的最新摘要以$ h $ free图表提供。
The NP-complete problem Matching Cut is to decide if a graph has a matching that is also an edge cut of the graph. We prove new complexity results for Matching Cut restricted to $H$-free graphs, that is, graphs that do not contain some fixed graph $H$ as an induced subgraph. We also prove new complexity results for two recently studied variants of Matching Cut, on $H$-free graphs. The first variant requires that the matching cut must be extendable to a perfect matching of the graph. The second variant requires the matching cut to be a perfect matching. In particular, we prove that there exists a small constant $r>0$ such that the first variant is NP-complete for $P_r$-free graphs. This addresses a question of Bouquet and Picouleau (arXiv, 2020). For all three problems, we give state-of-the-art summaries of their computational complexity for $H$-free graphs.
