Heavy fans, cycles and paths in weighted graphs of large connectivity
โ Scribed by Jun Fujisawa
- Book ID
- 108113679
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 301 KB
- Volume
- 307
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract Let __G__ be a simple graph of order __n__ and minimal degree >โcn (0โ<โcโ<โ1/2). We prove that (1) There exist __n__~0~โ=โ__n__~0~(__c__) and __k__โ=โ__k__(__c__) such that if __n__โ>โ__n__~0~ and __G__ contains a cycle __C__~__t__~ for some __t__โ>โ2__k__, then __G__ contains a cycle
## 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
Let G be a 2-connected weighted graph and k โฅ 2 an integer. In this note we prove that if the sum of the weighted degrees of every k + 1 pairwise nonadjacent vertices is at least m, then G contains either a cycle of weight at least 2m/(k + 1) or a spanning tree with no more than k leaves.