List Homomorphisms and Circular Arc Graphs
List Homomorphisms and Circular Arc Graphs
复制标题
列出同态和圆弧图
DOI：
10.1007/s004939970003
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发表时间：
1999
期刊：
影响因子：
1.1
通讯作者：
Jing Huang
中科院分区：
文献类型：
--
作者：
T. Feder;P. Hell;Jing Huang
g，h和列表，g，gwith to to listsl的列表同构是一个映射，因此所有人以及所有人都为此。固定图H的列表同构问题询问输入图g是否与列表一起，在较早的论文中介绍了列表的同构同构问题，并证明了反射图的同构列表同态问题。 h（即，对于每个顶点都有一个循环的图形h），如果h是间隔图，则可以求解多项式时间，否则为NP完整。在这里，我们考虑了无环的图形H，并发现该问题与圆形弧形密切相关。我们表明，如果H的补体是覆盖第二的集团的圆形弧形图，则列表同态问题是多项式时间的，并且否则为NP完整。出于证明的目的，由于没有类似于加莱的小行星类似的结构，我们给出了覆盖第二个集团的圆形弧形图的新表征。这两个结果都表明，间隔图与覆盖第二个集团的圆形弧形图之间的相似性令人惊讶。
G, H, and lists , a list homomorphism of G to Hwith respect to the listsL is a mapping , such that for all , and for all . The list homomorphism problem for a fixed graph H asks whether or not an input graph G together with lists , , admits a list homomorphism with respect to L. We have introduced the list homomorphism problem in an earlier paper, and proved there that for reflexive graphs H (that is, for graphs H in which every vertex has a loop), the problem is polynomial time solvable if H is an interval graph, and is NP-complete otherwise. Here we consider graphs H without loops, and find that the problem is closely related to circular arc graphs. We show that the list homomorphism problem is polynomial time solvable if the complement of H is a circular arc graph of clique covering number two, and is NP-complete otherwise. For the purposes of the proof we give a new characterization of circular arc graphs of clique covering number two, by the absence of a structure analogous to Gallai's asteroids. Both results point to a surprising similarity between interval graphs and the complements of circular arc graphs of clique covering number two.