𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Classifying 2-extendable generalized Petersen graphs

✍ Scribed by Qinglin Yu


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
559 KB
Volume
103
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


A graph is said to be 2-extendable if any two edges which do not have a common vertex are contained in a l-factor of the graph. In this paper, we show that the generalized Petersen graph GP(n, k) is 2-extandable for all n # 2k or 3k whenever k 2 3, as conjectured by Cammack and Schrag.


πŸ“œ SIMILAR VOLUMES


On the 2-extendability of the generalize
✍ Gerald Schrag; Larry Cammack πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 731 KB

A graph G is n-extendable if it is connected, contains a set of rr independent edges and every set of n-independent edges extends to (i.e. is a subset of) a perfect matching. Combining the results of this and previous papers we answer the question of 2-extendability for all the generalized Petersen

Which generalized petersen graphs are ca
✍ Roman Nedela; Martin Ε koviera πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 572 KB

## Abstract The generalized Petersen graph __GP__ (__n, k__), __n__ ≀ 3, 1 β‰₯ __k__ < __n__/2 is a cubic graph with vertex‐set {u~j~; i Ο΅ Z~n~} βˆͺ {v~j~; i Ο΅ Z~n~}, and edge‐set {u~i~u~i~, u~i~v~i~, v~i~v~i+k, iΟ΅~Z~n~}. In the paper we prove that (i) __GP__(__n, k__) is a Cayley graph if and only if

On 2-extendable abelian Cayley graphs
✍ Onn Chan; C.C. Chen; Qinglin Yu πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 737 KB

A graph G is 2-extendable if any two independent edges of G are contained in a perfect matching of G. A Cayley graph of even order over an abelian group is 2-extendable if and only if it is not isomorphic to any of the following circulant graphs: (I) Z2.(1,2n -1), n >~ 3; (II) ZE.(1,2,2n -1,2n -2),

On the crossing numbers of certain gener
✍ Dan McQuillan; R. Bruce Richter πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 484 KB

In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are

A Note on the Generalized Petersen Graph
✍ Marko Lovrečič SaraΕΎin πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 483 KB

The aim of this note is to present a short proof of a result of Nedela and S8 koviera (J. Graph Theory 19 (1995, 1 11)) concerning those generalized Petersen graphs that are also Cayley graphs. In that paper the authors chose the heavy weaponry of regular maps on closed connected orientable surfaces