Equitable Coloring in 1-Planar Graphs
Daniel Cranston, Reem Mahmoud
TL;DR
This paper proves that all 1-planar graphs with maximum degree at most r (for r ≥ 13) can be colored equitably with r colors, ensuring balanced color classes.
Contribution
It establishes a new equitable coloring result specifically for 1-planar graphs with high maximum degree, extending previous graph coloring theories.
Findings
Valid for all r ≥ 13
Applies to 1-planar graphs with degree constraints
Ensures equitable r-colorings
Abstract
For every , we show every 1-planar graph with has an equitable -coloring.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research