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
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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 -