5-choosability of graphs with 2 crossings
Victor Campos, Fr\'ed\'eric Havet
TL;DR
This paper proves that graphs with at most two crossings and graphs close to planar graphs are 5-choosable, extending understanding of graph colorability in nearly planar structures.
Contribution
It establishes new 5-choosability results for graphs with two crossings and graphs close to planar, broadening previous graph coloring theories.
Findings
Graphs with two crossings are 5-choosable.
Graphs that become planar upon removing one edge are 5-choosable.
Extends graph coloring results to nearly planar graphs.
Abstract
We show that every graph with two crossings is 5-choosable. We also prove that every graph which can be made planar by removing one edge is 5-choosable.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Computational Geometry and Mesh Generation