A note on ∆-critical graphs - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

A note on ∆-critical graphs


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.
Fichier principal
Vignette du fichier
DeltaCritical 15August2022.pdf (270.13 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03840737 , version 1 (06-11-2022)


  • HAL Id : hal-03840737 , version 1


Penny Haxell, Reza Naserasr. A note on ∆-critical graphs. 2022. ⟨hal-03840737⟩
15 View
1 Download


Gmail Facebook Twitter LinkedIn More