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arXiv · 1406.4718

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Jannis Bulian·Anuj Dawar
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Abstract

A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al. 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (2012).

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Jannis Bulian, Anuj Dawar. 2014-06-18. Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree. https://arxiv.org/abs/1406.4718

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