The Homomorphism Poset of K_3,3

2013/06/24 by Sally Cockburn, Cockburn, Sally
Engineering · Mathematics · #05C62 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05C62

paper · pdf · doi:10.48550/arxiv.1306.5732

8 pages, 4 figures

arxiv created 2013/06/24 · openalex publication_date 2013/06/24 · arxiv updated 2013/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A geometric graph \G is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call \G a geometric realization of the underlying abstract graph G. A geometric homomorphism from \G to \H is a vertex map that preserves adjacencies and crossings (but not necessarily non-adjacencies or non-crossings). Geometric homomorphisms can be used to define a partial order on the set of isomorphism classes of geometric realizations of an abstract graph G. In this paper, the homomorphism poset of K_3,3 is determined.

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