Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor
Arnott Kidner, Eckhard Steffen, Weiqiang Yu

TL;DR
This paper proves that all 4- and 5-regular projective planar graphs without Petersen minors can be properly edge-colored with r colors, extending understanding of edge-coloring in specific graph classes.
Contribution
It establishes that such graphs are r-edge colorable for r=4,5, a new result in the study of edge-coloring for these graph classes.
Findings
4- and 5-regular projective planar graphs without Petersen minors are r-edge colorable
The result extends edge-coloring theory to a new class of graphs
No Petersen-minor condition is crucial for the coloring property
Abstract
An -regular graph is an -graph, if every odd set of vertices is connected to its complement by at least edges. We prove for , every projective planar -graph with no Petersen-minor is -edge colorable.
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Taxonomy
TopicsAdvanced Graph Theory Research · Finite Group Theory Research · Limits and Structures in Graph Theory
