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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

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📜 SIMILAR VOLUMES


Supereulerian Graphs and the Petersen Gr
✍ Paul A. Catlin; Hong-Jian Lai 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 619 KB

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.

Locally petersen graphs
✍ J. I. Hall 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 684 KB

## 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

The spectrum problem for the Petersen gr
✍ Adams, Peter; Bryant, Darryn E. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 305 KB 👁 2 views

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.

On Petersen's graph theorem
✍ Nathan Linial 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 399 KB

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

Double cycle covers and the petersen gra
✍ Paul A. Catlin 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 711 KB

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

Which generalized petersen graphs are ca
✍ Roman Nedela; Martin Škoviera 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 572 KB

## 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