Reconfiguration of Cliques in a Graph
Reconfiguration of Cliques in a Graph
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DOI：
10.1007/978-3-319-17142-5_19
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Takehiro Ito;H. Ono;Y. Otachi
中科院分区：
文献类型：
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作者：
Takehiro Ito;H. Ono;Y. Otachi
我们研究了图中团的重构问题，确定是否存在一个团序列，该序列将一个给定的团以逐步的方式转换为另一个团。作为一个转换的一个步骤，我们考虑三种不同类型的规则，这是独立集的重新配置问题中定义和研究。我们首先证明这三个规则在团中是等价的。然后，我们证明了问题是PSPACE-完全的完美图，而我们给出了多项式时间算法的几类图，如偶孔自由图和cographs。特别是，最短的变体，计算所需序列的最短长度，可以在多项式时间内解决弦图，二分图，平面图和有界树宽图。
We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs.