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 $K_3 \lor E_6$.
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.
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol13/iss2/1