具有多项式可计算核的完美图
Perfect graphs with polynomially computable kernels
摘要：
在有向图中，核是稳定且吸收的顶点子集。不是所有的有向图都有核，但Boros和Gurvich的一个定理保证了完美图的每个无圈-无圈定向都有核。然而，一个悬而未决的问题是在这样的有向图的核计算的复杂性状况。我们的主要贡献是证明了完美图的子族的新的多项式性结果，其中包括无爪完美图和弦图。我们的研究结果是基于两个图形操作的核心计算方法的设计：cnc-割集分解和平坦边缘的增强。我们还证明了，决定存在的内核-计算它，如果它存在-是多项式在每个方向的弦或圆弧图，即使不是cyclo-acyclic。
英文摘要：
In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a perfect graph. However, an open question is the complexity status of the computation of a kernel in such a digraph. Our main contribution is to prove new polynomiality results for subfamilies of perfect graphs, among which are claw-free perfect graphs and chordal graphs. Our results are based on the design of kernel computation methods with respect to two graph operations: clique-cutset decomposition and augmentation of flat edges. We also prove that deciding the existence of a kernel - and computing it if it exists - is polynomial in every orientation of a chordal or a circular-arc graph, even not clique-acyclic.
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