Homomorphic Preimages of Geometric Cycles

A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism from G to H. A classic problem is to characterize the family of homomorphic preimages of a given graph H. A geometric graph is a simple graph G together with a straight line...

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Bibliographic Details
Published inarXiv.org
Main Author Cockburn, Sally
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.07.2015
Subjects
Apexes
Decision trees
Graph theory
Homomorphisms
Isomorphism
Mathematics - Combinatorics
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Summary:A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism from G to H. A classic problem is to characterize the family of homomorphic preimages of a given graph H. A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. A geometric homomorphism (resp. isomorphism) is a graph homomorphism (resp. isomorphism) that preserves edge crossings (resp. and non-crossings). The homomorphism posetof a graph G is the set of isomorphism classes of geometric realizations of G partially ordered by the existence of injective geometric homomorphisms. A geometric graph G is H-colorable if there is a geometric homomorphism from G to some element of the homomorphism poset of H. We provide necessary and sufficient conditions for a geometric graph to be C_n-colorable for n less than 6.
ISSN:2331-8422
DOI:10.48550/arxiv.1507.02758