识别单极图和2-次可着色图的参数化算法
Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs
摘要：
一个图$G$是一个$(Π_A,Π_B)$ -图，如果$V(G)$可以二分为$A$和$B$，使得$G[A]$满足性质$Π_A$，$G[B]$满足性质$Π_B$。$(Π_{A},Π_{B})$ -识别问题是识别给定图是否是$(Π_A,Π_B)$ -图。有许多$(Π_{A},Π_{B})$ -识别问题，包括识别问题的二部，分裂，和单极图。我们提出了有效的算法，许多情况下的$(Π_A,Π_B)$ -识别的基础上，我们称之为归纳识别的技术。特别地，我们给出了两个NP难的$(Π_{A},Π_{B})$ -识别问题，单极识别和2-子着色的固定参数算法。我们补充我们的算法结果与几个硬度结果$(Π_{A},Π_{B})$ -识别。
英文摘要：
A graph $G$ is a $(Π_A,Π_B)$-graph if $V(G)$ can be bipartitioned into $A$ and $B$ such that $G[A]$ satisfies property $Π_A$ and $G[B]$ satisfies property $Π_B$. The $(Π_{A},Π_{B})$-Recognition problem is to recognize whether a given graph is a $(Π_A,Π_B)$-graph. There are many $(Π_{A},Π_{B})$-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of $(Π_A,Π_B)$-Recognition based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard $(Π_{A},Π_{B})$-Recognition problems, Monopolar Recognition and 2-Subcoloring. We complement our algorithmic results with several hardness results for $(Π_{A},Π_{B})$-Recognition.
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