Ore-type conditions for the existence of even [2,b]-factors in graphs

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4 Citations (Scopus)

Abstract

For even b≥2, an even [2,b]-factor is a spanning subgraph each of whose degree is even between 2 and b. The main result is the following: a 2-edge-connected graph G of order n has an even [2,b]-factor if the degree sum of each pair of nonadjacent vertices in G is at least max⌈4n/(2+b), 5⌉. These lower bounds are best possible in some sense. The condition "2-edge-connected" cannot be dropped. This result was conjectured by Kouider and Vestergaard, and also is related to the study of Hamilton cycles, connected factors, spanning k-walks, and supereulerian graphs. Moreover, a related open problem is posed.

Original languageEnglish
Pages (from-to)51-61
Number of pages11
JournalDiscrete Mathematics
Volume304
Issue number1-3
DOIs
Publication statusPublished - 2005 Nov 28

Keywords

  • Cycle
  • Even factor
  • Factor
  • Trail
  • Walk

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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