Variable degeneracy: Extensions of Brooks' and Gallai's theorems

O. V. Borodin, A. V. Kostochka, B. Toft

Research output: Contribution to journalArticlepeer-review


We introduce the concept of variable degeneracy of a graph extending that of k-degeneracy. This makes it possible to give a common generalization of the point partition numbers and the list chromatic number. In particular, the list point arboricity of a graph is considered. We extend Brooks' and Gallai's theorems in terms of covering the vertices of a graph by disjoint induced subgraphs G1,...,Gs such that Gi is strictly fi-degenerate, given nonnegative-integer-valued functions f1,...,fs whose sum is bounded below at each vertex by the degree of that vertex.

Original languageEnglish (US)
Pages (from-to)101-112
Number of pages12
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Mar 21 2000
Externally publishedYes


  • Degeneracy
  • Graph colouring
  • List colouring
  • Point partition numbers
  • Vertex function

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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