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arXiv · 1805.01781

Morphism extension classes of countable $L$-colored graphs

Andrés Aranda·David Hartman
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Abstract

In~\cite{Hartman:2014}, Hartman, Hubi\v cka and Ma\v sulovi\'c studied the hierarchy of morphism extension classes for finite $L$-colored graphs, that is, undirected graphs without loops where sets of colors selected from $L$ are assigned to vertices and edges. They proved that when $L$ is a linear order, the classes $MH_L$ and $HH_L$ coincide, and the same is true for vertex-uniform finite $L$-colored graphs when $L$ is a diamond. In this paper, we explore the same question for countably infinite $L$-colored graphs. We prove that $MH_L=HH_L$ if and only if $L$ is a linear order.

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Andrés Aranda, David Hartman. 2018-05-04. Morphism extension classes of countable $L$-colored graphs. https://arxiv.org/abs/1805.01781

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