On Graphs with Chromatic Number and Maximum Degree Both Equal to Nine

Authors

• Rachel Galindo, Auburn UniversityFollow
• Jessica McDonald, Auburn UniversityFollow

Publication Date

October 2026

Abstract

An equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with $\chi = \Delta = 9$ contains $K_3 \lor E_6$ as a subgraph. Here we prove several results in support of this conjecture, where vertex-criticality and forbidden substructure conditions get us either close or all the way to containing $K_3 \lor E_6$.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Galindo, Rachel and McDonald, Jessica (2026) "On Graphs with Chromatic Number and Maximum Degree Both Equal to Nine," Theory & Applications of Graphs: Vol. 13: Iss. 2, Article 1.
DOI: 10.20429/tag.2026.130201
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol13/iss2/1