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Graph Isomorphism for $$(H_1,H_2)$$-Free Graphs: An Almost Complete Dichotomy
Algorithmica ( IF 1.1 ) Pub Date : 2020-08-05 , DOI: 10.1007/s00453-020-00747-x Marthe Bonamy , Nicolas Bousquet , Konrad K. Dabrowski , Matthew Johnson , Daniël Paulusma , Théo Pierron
Algorithmica ( IF 1.1 ) Pub Date : 2020-08-05 , DOI: 10.1007/s00453-020-00747-x Marthe Bonamy , Nicolas Bousquet , Konrad K. Dabrowski , Matthew Johnson , Daniël Paulusma , Théo Pierron
We resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H_{1} $$\end{document} and H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_2$$\end{document} for all but six pairs (H1,H2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(H_1,H_2)$$\end{document}. 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 clique-width. 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 (H1,H2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(H_1,H_2)$$\end{document}-free graphs to five.
中文翻译:
$$(H_1,H_2)$$-Free 图的图同构:几乎完全二分法
H2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin }{-69pt} \begin{document}$$(H_1,H_2)$$\end{document}。Schweitzer 之前曾表明开放案例的数量是有限的,但没有具体说明开放案例。Grohe 和 Schweitzer 证明了图同构在有界团宽的图类上是多项式时间可解的。我们的工作将诸如此类的已知结果与新结果相结合。通过利用图同构和集团宽度之间的关系,我们同时减少了 (H1,
更新日期:2020-08-05
中文翻译:
$$(H_1,H_2)$$-Free 图的图同构:几乎完全二分法
H2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin }{-69pt} \begin{document}$$(H_1,H_2)$$\end{document}。Schweitzer 之前曾表明开放案例的数量是有限的,但没有具体说明开放案例。Grohe 和 Schweitzer 证明了图同构在有界团宽的图类上是多项式时间可解的。我们的工作将诸如此类的已知结果与新结果相结合。通过利用图同构和集团宽度之间的关系,我们同时减少了 (H1,