Isomorphism Testing for T-graphs in FPT

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00125687" target="_blank" >RIV/00216224:14330/22:00125687 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-96731-4_20" target="_blank" >http://dx.doi.org/10.1007/978-3-030-96731-4_20</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-96731-4_20" target="_blank" >10.1007/978-3-030-96731-4_20</a>

Result language
angličtina
Original language name
Isomorphism Testing for T-graphs in FPT
Original language 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].
Czech name
—
Czech description
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Project
<a href="/en/project/GA20-04567S" target="_blank" >GA20-04567S: Structure of tractable instances of hard algorithmic problems on graphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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