(2, 3)-bipartite graphs are strongly 6-edge-choosable
Petru Valicov
TL;DR
This paper provides a shorter proof that certain bipartite graphs derived from cubic graphs are strongly 6-edge-choosable, advancing understanding in graph coloring and choosability.
Contribution
It offers a more concise proof of the strong 6-edge-choosability of (2,3)-bipartite graphs, building on prior results about cubic graphs.
Findings
Shorter proof of strong 6-edge-choosability for (2,3)-bipartite graphs
Connections between cubic graph properties and bipartite graph coloring
Enhanced understanding of edge-choosability in bipartite graphs
Abstract
Kang and Park recently showed that every cubic (loopless) multigraph is incidence 6-choosable [On incidence choosability of cubic graphs. \emph{arXiv}, April 2018]. Equivalently, every bipartite graph obtained by subdividing once every edge of a cubic graph, is strongly 6-edge-choosable. The aim of this note is to give a shorter proof of their result by looking at the strong edge-coloring formulation of the problem.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems