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arXiv · 1002.1749

On graph equivalences preserved under extensions

Zbigniew Lonc·Miroslaw Truszczynski
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Abstract

Let R be an equivalence relation on graphs. By the strengthening of R we mean the relation R' such that graphs G and H are in the relation R' if for every graph F, the union of the graphs G and F is in the relation R with the union of the graphs H and F. We study strengthenings of equivalence relations on graphs. The most important case that we consider concerns equivalence relations defined by graph properties. We obtain results on the strengthening of equivalence relations determined by the properties such as being a k-connected graph, k-colorable, hamiltonian and planar.

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Zbigniew Lonc, Miroslaw Truszczynski. 2010-02-09. On graph equivalences preserved under extensions. https://arxiv.org/abs/1002.1749

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