Algorithms solving the Matching Cut problem

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• 作者：Dieter Kratsch^a ; ^{kratsch@univ-metz.fr" class="auth_mail" title="E-mail the corresponding author} ; Van Bang Le^b ; ^{van-bang.le@uni-rostock.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Matching cut ; Graph algorithm
• 刊名：Theoretical Computer Science
• 出版年：2016
• 出版时间：4 January 2016
• 年：2016
• 卷：609
• 期：part_P2
• 页码：328-335
• 全文大小：336 K

文摘

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete. This paper provides a first branching algorithm solving Matching Cut in time O^⁎(2^n/2)=O^⁎(1.4143ⁿ)$O^{⁎}(2^{n/2})=O^{⁎}({1.4143}^n)$ for an n-vertex input graph, and shows that Matching Cut parameterized by the vertex cover number ccdfb2aa60" title="Click to view the MathML source">τ(G)$\tau (G)$ can be solved by a single-exponential algorithm in time 2^τ(G)O(n²)$2^{\tau (G)}O(n^2)$. Moreover, the paper also gives a polynomially solvable case for Matching Cut which covers previous known results on graphs of maximum degree three, line graphs, and claw-free graphs.