Subcubic planar graphs of girth 7 are class I
Sebastien Bonduelle, Franti\v{s}ek Kardo\v{s}
TL;DR
This paper proves that planar graphs with maximum degree 3 and girth at least 7 can be edge-colored with three colors, extending earlier results for girth at least 8.
Contribution
It extends the class of planar graphs known to be 3-edge-colorable to those with girth at least 7, improving previous bounds.
Findings
Planar graphs with max degree 3 and girth ≥7 are 3-edge-colorable.
Extends previous girth bound from 8 to 7.
Provides new proof techniques for edge-colorability.
Abstract
We prove that planar graphs of maximum degree 3 and of girth at least 7 are 3-edge-colorable, extending the previous result for girth at least 8 by Kronk, Radlowski, and Franen from 1974.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research