Articles by Jonathan Narboni

On the Structure of Potential Counterexamples to the Borodin-Kostochka Conjecture

-- Jonathan Narboni (LaBRI)

summary: The Borodin-Kostochka conjecture, a long-standing problem in graph theory, asserts that every graph \(G\) with maximum degree \(\Delta \geq 9\) satisfies \(\chi(G) \leq max \{\Delta - 1, \omega(G)\}\) where \(\chi(G)\) and \(\omega(G)\) are respectively the chromatic number and the clique number of \(G\). While the conjecture ...