• Medientyp: E-Artikel
  • Titel: A Note on Vertex List Colouring
  • Beteiligte: HAXELL, P. E.
  • Erschienen: Cambridge University Press (CUP), 2001
  • Erschienen in: Combinatorics, Probability and Computing, 10 (2001) 4, Seite 345-347
  • Sprache: Englisch
  • DOI: 10.1017/s0963548301004758
  • ISSN: 0963-5483; 1469-2163
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: Let k be a positive integer and let G be a graph. Suppose a list S(v) of positive integers is assigned to each vertex v, such that(1) [mid ]S(v)[mid ] = 2k for each vertex v of G, and(2) for each vertex v, and each c ∈ S(v), the number of neighbours w of v for which c ∈ S(w) is at most k.Then we prove that there exists a proper vertex colouring f of G such that f(v) ∈ S(v) for each v ∈ V(G). This proves a weak version of a conjecture of Reed.