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Long Cycles Passing Through a Specified Edge in 3-Connected Graphs

โœ Scribed by Zhiren Sun; Feng Tian; Bing Wei

Publisher
Springer Japan
Year
2001
Tongue
English
Weight
157 KB
Volume
17
Category
Article
ISSN
0911-0119

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๐Ÿ“œ SIMILAR VOLUMES

Long cycles passing through a specified
Long cycles passing through a specified edge in a 3-connected graph
โœ Enomoto, Hikoe; Hirohata, Kazuhide; Ota, Katsuhiro ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 80 KB ๐Ÿ‘ 2 views

We prove the following theorem: For a connected noncomplete graph Then through each edge of G there passes a cycle of length โ‰ฅ min{|V (G)|, ฯ„(G) -1}.

Long cycles passing through a specified
Long cycles passing through a specified path in a graph
โœ Hirohata, Kazuhide ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 247 KB ๐Ÿ‘ 2 views

## For a graph G and an integer an independent set of vertices in G}. Enomoto proved the following theorem. Let s โ‰ฅ 1 and let G be a (s + 2)-connected graph. Then G has a cycle of length โ‰ฅ min{|V (G)|, ฯƒ 2 (G) -s} passing through any path of length s. We generalize this result as follows. Let k โ‰ฅ

Heavy cycles passing through some specif
Heavy cycles passing through some specified vertices in weighted graphs
โœ Jun Fujisawa; Kiyoshi Yoshimoto; Shenggui Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 111 KB

## Abstract A weighted graph is one in which every edge __e__ is assigned a nonnegative number, called the weight of __e__. The sum of the weights of the edges incident with a vertex ฯ… is called the weighted degree of ฯ…. The weight of a cycle is defined as the sum of the weights of its edges. In th

Long Cycles in 3-Connected Graphs
Long Cycles in 3-Connected Graphs
โœ Guantao Chen; Xingxing Yu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 249 KB

Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Oรฐn log 3 2 รž: In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus