A graph G is (n, \*)-connected if it satisfies the following conditions: (1) |V(G)| n+1; (2) for any subset S V(G) and any subset L E(G) with \* |S| +|L| <n\*, G&S&L is connected. The (n, \*)-connectivity is a common extension of both the vertex-connectivity and the edge-connectivity. An (n, 1)-conn
Note on Halin's theorem on minimally connected graphs
β Scribed by T Kameda
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 205 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Hartnell, B.L. and W. Kocay, On minimal neighbourhood-connected graphs, Discrete Mathematics 92 (1991) 95-105. The closed neighbourhood of a vertex u of a graph G is u\* = {v 1 v is adjacent to u} U {u}. G is neighbourhood-connected if it is connected, and G -u' is connected but not complete, for al
## Abstract An edge of a 5βconnected graph is said to be contractible if the contraction of the edge results in a 5βconnected graph. Let __x__ be a vertex of a 5βconnected graph. We prove that if there are no contractible edges whose distance from __x__ is two or less, then either there are two tri
In thiq paper we prove the following: let G be a graph with k edges, wihich js (k -l)-edgeconnectd, and with all valences 3k k. Let 1 c r~ k be an integer, then (3 -tins a spanning subgraph H, so that all valences in H are ar, with no more than r~/r:] edges. The proof is based on a useful extension