Making a graph crossing-critical by multiplying its edges
Combinatorics
2011-12-20 v3
Abstract
A graph is crossing-critical if the removal of any of its edges decreases its crossing number. This work is motivated by the following question: to what extent is crossing- criticality a property that is inherent to the structure of a graph, and to what extent can it be induced on a noncritical graph by multiplying (all or some of) its edges? It is shown that if a nonplanar graph G is obtained by adding an edge to a cubic polyhedral graph, and G is sufficiently connected, then G can be made crossing-critical by a suitable multiplication of edges.
Keywords
Cite
@article{arxiv.1112.3167,
title = {Making a graph crossing-critical by multiplying its edges},
author = {Laurent Beaudou and César Hernández-Vélez and Gelasio Salazar},
journal= {arXiv preprint arXiv:1112.3167},
year = {2011}
}
Comments
12 pages - last proof updated