## Abstract In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Ξ is __n__β__HCβextendable__ if it contains a path of length __n__ and if every such path is contained in some Hamilton cycle of Ξ. Similarly, Ξ is __weakly n__β__HPβ
Hamilton-Connected Cayley Graphs on Hamiltonian Groups
β Scribed by Brian Alspach; Yusheng Qin
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 109 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
It is proven that every connected Cayley graph X , of valency at least three, on a Hamiltonian group is either Hamilton laceable when X is bipartite, or Hamilton connected when X is not bipartite.
π SIMILAR VOLUMES
In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian
Alspach has conjectured that any 2k-regular connected Cayley graph cay(A, S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S=[s 1 , s 2 , ..., s k ] is a minimal generating set of an abelian group A of odd order (where a
A Cayley graph or digraph Cay(G, S) of a finite group G is called a CI-graph of G if, for any T/G, Cay(G, S)$Cay(G, T) if and only if S \_ =T for some \_ # Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite group G is called a conne
The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.