Isomorphism Testing for T-graphs in FPT
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Proceedings |
| Conference | WALCOM: Algorithms and Computation |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-030-96731-4_20 |
| Keywords | chordal graph · H-graph · leafage · graph isomorphism · parameterized complexity |
| Description | 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 isomorphisminvariant decomposition of T-graphs with the classical tower-of-groups algorithm of Babai, and reuse some of the ideas of our isomorphism algorithm for Sd-graphs [MFCS 2020]. |
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