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 | |
| Publication status | Published - 2005 Nov 28 |
| Externally published | Yes |
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Keywords
- Cycle
- Even factor
- Factor
- Trail
- Walk
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
Cite this
Ore-type conditions for the existence of even [2,b]-factors in graphs. / Matsuda, Haruhide.
In: Discrete Mathematics, Vol. 304, No. 1-3, 28.11.2005, p. 51-61.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Ore-type conditions for the existence of even [2,b]-factors in graphs
AU - Matsuda, Haruhide
PY - 2005/11/28
Y1 - 2005/11/28
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=27944462759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=27944462759&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2005.09.009
DO - 10.1016/j.disc.2005.09.009
M3 - Article
AN - SCOPUS:27944462759
VL - 304
SP - 51
EP - 61
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 1-3
ER -