𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Long cycles in vertex-transitive graphs

✍ Scribed by László Babai


Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
192 KB
Volume
3
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

We prove that every connected vertex‐transitive graph on n ≥ 4 vertices has a cycle longer than (3__n__)^1/2^. The correct order of magnitude of the longest cycle seems to be a very hard question.


📜 SIMILAR VOLUMES


Vertex-transitive graphs that are not Ca
✍ McKay, Brendan D.; Praeger, Cheryl E. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 881 KB

The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph that is not a Cayley graph. In 1983, D. MaruSiE asked, "For what values of n does there exist such a graph on n vertices?" We give several new constructions of families of vertex-transitive graphs that are not Cay

On cubic non-Cayley vertex-transitive gr
✍ Klavdija Kutnar,; Dragan Marušič;; Cui Zhang 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB

## Abstract In 1983, the second author [D. Marušič, Ars Combinatoria 16B (1983), 297–302] asked for which positive integers __n__ there exists a non‐Cayley vertex‐transitive graph on __n__ vertices. (The term __non‐Cayley numbers__ has later been given to such integers.) Motivated by this problem,

Cubic vertex-transitive graphs of order
✍ Jin-Xin Zhou; Yan-Quan Feng 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 166 KB

A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite group and S a subset of G such that 1 / ∈ S and S = {s -1 | s ∈ S}. The Cayley graph Cay(G, S) on G with respect to S

Tetravalent vertex-transitive graphs of
✍ Jin-Xin Zhou 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB

A graph is __vertex‐transitive__ if its automorphism group acts transitively on vertices of the graph. A vertex‐transitive graph is a __Cayley graph__ if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex‐transitive non‐Cayley graphs

Long cycles in critical graphs
✍ Noga Alon; Michael Krivelevich; Paul Seymour 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 57 KB 👁 3 views