Any 3-edge-connected graph with at most 10 edge cuts of size 3 either has a spanning closed trail or it is contractible to the Petersen graph.
The ubiquitous Petersen graph
✍ Scribed by Gary Chartrand; Héctor Hevia; Robin J. Wilson
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 507 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract A graph Γ is locally Petersen if, for each point __t__ of Γ, the graph induced by Γ on all points adjacent to __t__ is isomorphic to the Petersen graph. We prove that there are exactly three isomorphism classes of connected, locally Petersen graphs and further characterize these graphs
It is shown that there exists a decomposition of K,, into edge-disjoint copies of the Petersen graph if and only if 'u = 1 or 10 (mod 151, 'u # 10.
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
Let O(G) denote the set of odd-degree vertices of a graph G. Let t E N and let 9, denote the family of graphs G whose edge set has a partition This partition is associated with a double cycle cover of G. We show that if a graph G is at most 5 edges short of being 4-edge-connected, then exactly one
## Abstract The generalized Petersen graph __GP__ (__n, k__), __n__ ≤ 3, 1 ≥ __k__ < __n__/2 is a cubic graph with vertex‐set {u~j~; i ϵ Z~n~} ∪ {v~j~; i ϵ Z~n~}, and edge‐set {u~i~u~i~, u~i~v~i~, v~i~v~i+k, iϵ~Z~n~}. In the paper we prove that (i) __GP__(__n, k__) is a Cayley graph if and only if