Coloring $(P_5, \text{gem})$-free graphs with $\Delta -1$ colors

Daniel W. Cranston; Hudson Lafayette; Landon Rabern

doi:10.1002/jgt.22845

Coloring $(P_5, \text{gem})$-free graphs with $\Delta -1$ colors

Combinatorics 2024-12-06 v1

Authors: Daniel W. Cranston , Hudson Lafayette , Landon Rabern

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Abstract

The Borodin-Kostochka Conjecture states that for a graph $G$ , if $\Delta(G) \geq 9$ and $\omega(G) \leq \Delta(G)-1$ , then $\chi(G)\leq\Delta(G) -1$ . We prove the Borodin-Kostochka Conjecture for $(P_5, \text{gem})$ -free graphs, i.e., graphs with no induced $P_5$ and no induced $K_1\vee P_4$ .

Keywords

hadwiger conjecture graph coloring graph theory

Cite

@article{arxiv.2006.02015,
  title  = {Coloring $(P_5, \text{gem})$-free graphs with $\Delta -1$ colors},
  author = {Daniel W. Cranston and Hudson Lafayette and Landon Rabern},
  journal= {arXiv preprint arXiv:2006.02015},
  year   = {2024}
}

Comments

8 pages, 6 figures

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