TY - JOUR
T1 - Weighted degrees and heavy cycles in weighted graphs
AU - Fujisawa, Jun
PY - 2009/12/6
Y1 - 2009/12/6
N2 - A weighted graph is a graph provided with an edge-weighting functionw from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53-69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to an Ore-type one in unweighted graphs, it is shown in Bondy et al. [Discuss. Math. Graph Theory 22 (2002), 7-15] that Bondy and Fan's theorem, which uses Dirac-type condition, cannot be generalized analogously by using Ore-type condition. In this paper we investigate the property peculiar to weighted graphs, and prove a theorem on the existence of heavy cycles in weighted graphs under an Ore-type condition, which generalizes Bondy and Fan's theorem. Moreover, we show the existence of heavy cycles passing through some specified vertices.
AB - A weighted graph is a graph provided with an edge-weighting functionw from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53-69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to an Ore-type one in unweighted graphs, it is shown in Bondy et al. [Discuss. Math. Graph Theory 22 (2002), 7-15] that Bondy and Fan's theorem, which uses Dirac-type condition, cannot be generalized analogously by using Ore-type condition. In this paper we investigate the property peculiar to weighted graphs, and prove a theorem on the existence of heavy cycles in weighted graphs under an Ore-type condition, which generalizes Bondy and Fan's theorem. Moreover, we show the existence of heavy cycles passing through some specified vertices.
KW - Heavy cycle
KW - Weighted degree
KW - Weighted graph
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U2 - 10.1016/j.disc.2009.06.020
DO - 10.1016/j.disc.2009.06.020
M3 - Article
AN - SCOPUS:70350604253
VL - 309
SP - 6483
EP - 6495
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 23-24
ER -