An extremal problem in subconnectivity
β Scribed by F. T. Boesch; J. A. M. McHugh
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 186 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0894-069X
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π SIMILAR VOLUMES
It is proved that every graph G with G β₯ 2|G| -5, |G| β₯ 6, and girth at least 5, except the Petersen graph, contains a subdivision of K - 5 , the complete graph on five vertices minus one edge.
Let r, t 2 2 be integers and c a constant, 0 < c 5 ( r -2 ) / ( r -1). Suppose that G is a &-free graph on n vertices in which any t distinct vertices have at most cn common neighbors. Here an asymptotically best bound is obtained for the maximal number of edges in such graphs. This solves a problem
## Abstract We introduce the notion of __H__βlinked graphs, where __H__ is a fixed multigraph with vertices __w__~1~,β¦,__w__~m~. A graph __G__ is __H__β__linked__ if for every choice of vertices Ο ~1~,β¦, Ο ~m~ in __G__, there exists a subdivision of __H__ in __G__ such that Ο ~i~ is the branch vertex