Revisiting a theorem by Folkman on graph colouring

Marthe Bonamy (1) , Pierre Charbit (2) , Oscar Defrain (3) , Gwénaël Joret (4) , Aurélie Lagoutte (3) , Vincent Limouzy (3) , Lucas Pastor (3) , Jean-Sébastien Sereni (5)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 Département d'Informatique
5 CNRS - Centre National de la Recherche Scientifique

We give a short proof of the following theorem due to Jon H. Folkman (1969): The chromatic number of any graph is at most 2 plus the maximum over all subgraphs of the difference between the number of vertices and twice the independence number.

Domaines: Combinatoire [math.CO]

Marthe Bonamy, Pierre Charbit, Oscar Defrain, Gwénaël Joret, Aurélie Lagoutte, et al.. Revisiting a theorem by Folkman on graph colouring. The Electronic Journal of Combinatorics, 2020, 27 (1), pp.P1.56. ⟨10.37236/8899⟩. ⟨hal-02194900v2⟩