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

Haruhide Matsuda

doi:10.1016/j.disc.2005.09.009

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

Haruhide Matsuda

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Pages (from-to)	51-61
Number of pages	11
Journal	Discrete Mathematics
Volume	304
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2005.09.009
Publication status	Published - 2005 Nov 28
Externally published	Yes

Keywords

Cycle
Even factor
Factor
Trail
Walk

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2005.09.009

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AB - 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.

KW - Cycle

KW - Even factor

KW - Factor

KW - Trail

KW - Walk

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

Abstract

Keywords

ASJC Scopus subject areas

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