Coloring plane graphs with independent crossings
Daniel Kr\'al', Ladislav Stacho
TL;DR
This paper proves that certain plane graphs with specific face and crossing properties are 5-colorable, addressing a question about the colorability of graphs with independent crossings.
Contribution
It establishes that plane graphs with maximum face size four and disjoint quadrilateral faces are cyclically 5-colorable, answering a question about graphs with independent crossings.
Findings
Graphs with maximum face size four and disjoint quadrilateral faces are cyclically 5-colorable
Addresses a question about 5-colorability of graphs with independent crossings
Provides a new result in graph coloring related to plane graphs
Abstract
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5-colorable.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems