Cycles through edges in cyclically k–connected cubic graphs
✍ Scribed by William McCuaig
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 247 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
McCuaig, W., Cycles through edges in cyclically k-connected cubic graphs
📜 SIMILAR VOLUMES
## Abstract In this article, we prove the following theorem. Let __k__ ≥ 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
## Abstract We show that every __k__‐connected graph with no 3‐cycle contains an edge whose contraction results in a __k__‐connected graph and use this to prove that every (__k__ + 3)‐connected graph contains a cycle whose deletion results in a __k__‐connected graph. This settles a problem of L. Lo
## Abstract It is shown that some classes of cyclically 5‐edge‐connected cubic planar graphs with only one type of face besides pentagons contain non‐Hamiltonian members and have shortness coefficients less than unity.
P ósa proved that if G is an n-vertex graph in which any two nonadjacent vertices have degree-sum at least n+k, then G has a spanning cycle containing any specified family of disjoint paths with a total of k edges. We consider the analogous problem for a bipartite graph G with n vertices and parts o