A T-graph (a special case of a chordal graph) is the intersection graph of connected subtrees of a suitable subdivision of a fixed tree T . We deal with the isomorphism problem for T-graphs which is GI-complete in general - when T is a part of the input and even a star. We prove that the T-graph isomorphism problem is in FPT when T is the fixed parameter of the problem. This can equivalently be stated that isomorphism is in FPT for chordal graphs of (so-called) bounded leafage. While the recognition problem for T-graphs is not known to be in FPT wrt. T, we do not need a T-representation to be given (a promise is enough). To obtain the result, we combine a suitable isomorphism-invariant decomposition of T-graphs with the classical tower-of-groups algorithm of Babai, and reuse some of the ideas of our isomorphism algorithm for S_d-graphs [MFCS 2020].
翻译:Tgraph (Chordal 图形的一个特例) 是固定树T适当分区连接的小树的相联亚树的交叉图。 我们处理Tgraph 的异形问题, 一般来说, T是输入的一部分, 甚至是一个恒星。 我们证明, Tgraph 的异形问题在FPT 中, T是问题的固定参数。 这可以说, 在FPT 中, (所谓的) 捆绑的叶的相形形形形形形形形形形形形形形形形形形形形形形形形形形形形形色形形形形形形形形形形形形形形形形形色色色色形色色色形形形形色色形形形形色形形色色形色色色色色色色色色色色色色色色色色色色色色色色的图。 虽然Trababai 古典图(MFCS 2020) 并重新使用我们S_d-d-d-graph 算法的一些想法。 T, 我们不需要的图形形形形形形形形形形形形形形形图式图式图式图式图式图状色色图式图式图式图状图式图(MFMFFFCS-CS-2020 2020 2020 2020)。