Graph Isomorphism for (H-1, H-2)-Free Graphs: An Almost Complete Dichotomy

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00121465" target="_blank" >RIV/00216224:14330/21:00121465 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00453-020-00747-x" target="_blank" >https://doi.org/10.1007/s00453-020-00747-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00453-020-00747-x" target="_blank" >10.1007/s00453-020-00747-x</a>

Result language
angličtina
Original language name
Graph Isomorphism for (H-1, H-2)-Free Graphs: An Almost Complete Dichotomy
Original language description
We resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs H-1 and H-2 for all but six pairs (H-1, H-2). Schweitzer had previously shown that the number of open cases was finite, but without specifying the open cases. Grohe and Schweitzer proved that Graph Isomorphism is polynomial-time solvable on graph classes of bounded cliquewidth. Our work combines known results such as these with new results. By exploiting a relationship between Graph Isomorphism and clique-width, we simultaneously reduce the number of open cases for boundedness of clique-width for (H-1, H-2)-free graphs to five.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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