Graphs with girth 9 and without longer odd holes are 3-colorable
Yan Wang, Rong Wu

TL;DR
This paper proves that graphs with girth 9 and no longer odd holes are 3-colorable, confirming a conjecture that all such graphs in a certain family are 3-colorable.
Contribution
The paper proves Wu, Xu, and Xu's conjecture for the case l=4, establishing 3-colorability for graphs with girth 9 and no longer odd holes.
Findings
Graphs in ${ m{ extbf{G}}}_4$ are 3-colorable.
Confirms Wu, Xu, and Xu's conjecture for l=4.
Extends known results to a new family of graphs.
Abstract
For a number , let denote the family of graphs which have girth and have no odd hole with length greater than . Wu, Xu and Xu conjectured that every graph in is -colorable. Chudnovsky et al., Wu et al., and Chen showed that every graph in , and is -colorable respectively. In this paper, we prove that every graph in is -colorable. This confirms Wu, Xu and Xu's conjecture.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems
