TY - JOUR
T1 - Heavy fans, cycles and paths in weighted graphs of large connectivity
AU - Fujisawa, Jun
N1 - Funding Information:
The author would like to thank Professors Hajo Broersma and Katsuhiro Ota for their valuable suggestions and helpful comments. This work was partially supported by the JSPS Research Fellowships for Young Scientists and the 21st Century COE Program; Integrative Mathematical Sciences: Progress in Mathematics Motivated by Social and Natural Sciences.
PY - 2007/1/6
Y1 - 2007/1/6
N2 - A set of paths joining a vertex y and a vertex set L is called (y, L)-fan if any two of the paths have only y in common, and its width is the number of paths forming it. In weighted graphs, it is known that the existence of heavy fan is useful to find a heavy cycle containing some specified vertices. In this paper, we show the existence of heavy fans with large width containing some specified vertices in weighted graphs of large connectivity, which is a weighted analogue of Perfect's theorem. Using this, in 3-connected weighted graphs, we can find heavy cycles containing three specified vertices, and also heavy paths joining two specified vertices containing two more specified vertices. These results extend the previous results in 2-connected weighted graphs to 3-connected weighted graphs.
AB - A set of paths joining a vertex y and a vertex set L is called (y, L)-fan if any two of the paths have only y in common, and its width is the number of paths forming it. In weighted graphs, it is known that the existence of heavy fan is useful to find a heavy cycle containing some specified vertices. In this paper, we show the existence of heavy fans with large width containing some specified vertices in weighted graphs of large connectivity, which is a weighted analogue of Perfect's theorem. Using this, in 3-connected weighted graphs, we can find heavy cycles containing three specified vertices, and also heavy paths joining two specified vertices containing two more specified vertices. These results extend the previous results in 2-connected weighted graphs to 3-connected weighted graphs.
KW - Heavy cycle
KW - Heavy path
KW - Perfect's theorem
KW - Specified vertex
KW - Weighted graph
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U2 - 10.1016/j.disc.2006.04.036
DO - 10.1016/j.disc.2006.04.036
M3 - Article
AN - SCOPUS:33751209482
SN - 0012-365X
VL - 307
SP - 38
EP - 53
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1
ER -