Cycles and paths through specified vertices in k-connected graphs
β 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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π SIMILAR VOLUMES
## Abstract In this article, we prove the following theorem. Let __k__ββ₯β3 be an integer, __G__ be a __k__βconnected graph with minimum degree __d__ and __X__ be a set of __k__β+β1 vertices on a cycle. Then __G__ has a cycle of length at least min {2d,|V(G)|} passing through __X__. This result give
## 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
## Abstract We show that every set of $k+\lfloor{1\over 3}\sqrt{k}\rfloor$ vertices in a __k__βconnected __k__βregular graph belongs to some circuit. Β© 2002 John Wiley & Sons, Inc. J Graph Theory 39: 145β163, 2002
## 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)|, Ο 2 (G) -s} passing through any path of length s. We generalize this result as follows. Let k β₯