A note on ∆-critical graphs
Résumé
A k-critical graph is a k-chromatic graph whose proper subgraphs are all (k − 1)colourable. An old open problem due to Borodin and Kostochka asserts that for k ≥ 9, no k-critical graph G with k = ∆(G) exists, where ∆(G) denotes the maximum degree of G. We show that if a certain special list-colouring property holds for every 8-critical graph with ∆ = 8 (which is true for the apparently only known example) then the Borodin-Kostochka Conjecture holds. We also briefly survey constructions of ∆-critical graphs with ∆ ≤ 8, highlighting the apparent scarcity of such graphs once ∆ exceeds 6.
Domaines
Mathématique discrète [cs.DM]Origine | Fichiers produits par l'(les) auteur(s) |
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