Classes of 3-regular graphs that are (7, 2)-edge-choosable
Daniel W. Cranston, Douglas B. West
TL;DR
This paper investigates the (7, 2)-edge-choosability of 3-regular graphs, establishing that all 3-edge-colorable graphs and many non-3-edge-colorable ones possess this property, expanding understanding of list edge-coloring.
Contribution
It proves that all 3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable and identifies many non-3-edge-colorable 3-regular graphs with this property.
Findings
All 3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.
Many non-3-edge-colorable 3-regular graphs are also (7, 2)-edge-choosable.
The results extend the class of graphs known to be (7, 2)-edge-choosable.
Abstract
A graph is (7, 2)-edge-choosable if, for every assignment of lists of size 7 to the edges, it is possible to choose two colors for each edge from its list so that no color is chosen for two incident edges. We show that every 3-edge-colorable graph is (7, 2)-edge-choosable and also that many non-3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph Labeling and Dimension Problems · graph theory and CDMA systems