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arXiv · 1010.2047

Foldings in graphs and relations with simplicial complexes and posets

Etienne Fieux·Jacqueline Lacaze
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Abstract

We study dismantlability in graphs. In order to compare this notion to similar operations in posets (partially ordered sets) or in simplicial complexes, we prove that a graph G dismants on a subgraph H if and only if H is a strong deformation retract of G. Then, by looking at a triangle relating graphs, posets and simplicial complexes, we get a precise correspondence of the various notions of dismantlability in each framework. As an application, we study the link between the graph of morphisms from a graph G to a graph H and the polyhedral complex Hom(G,H); this gives a more precise statement about well known results concerning the polyhedral complex Hom(G,H) and its relation with foldings in G or H.

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Etienne Fieux, Jacqueline Lacaze. 2010-10-11. Foldings in graphs and relations with simplicial complexes and posets. https://arxiv.org/abs/1010.2047

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