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Cycles and paths through specified vertices in k-connected graphs

✍ Scribed by Y Egawa; R Glas; S.C Locke


Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
693 KB
Volume
52
Category
Article
ISSN
0095-8956

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Cycles passing through k + 1 vertices in
✍ Jun Fujisawa; Tomoki Yamashita πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 149 KB πŸ‘ 1 views

## Abstract In this article, we prove the following theorem. Let __k__ β‰₯ 3 be an integer, __G__ be a __k__‐connected graph with minimum degree __d__ and __X__ be a set of __k__ + 1 vertices on a cycle. Then __G__ has a cycle of length at least min {2d,|V(G)|} passing through __X__. This result give

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## 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 Ο… is called the weighted degree of Ο…. The weight of a cycle is defined as the sum of the weights of its edges. In th

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## Abstract We show that every set of $k+\lfloor{1\over 3}\sqrt{k}\rfloor$ vertices in a __k__‐connected __k__‐regular graph belongs to some circuit. Β© 2002 John Wiley & Sons, Inc. J Graph Theory 39: 145–163, 2002

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