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
Edge-hamiltonian property in regular 2- connected graphs
β Scribed by Hao Li
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 515 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Bill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is hamiltonian.
It is shown in this paper that, under almost the same conditions as above, the graphs are edge-hamiltonian.
π SIMILAR VOLUMES
Let G be a 2-edge connected graph with a t least 5 vertices. For any given vertices a, b, c, and din G with a # b, there exists in G3 a hamiltonian path with endpoints a and b avoiding the edge cd, and there exists in G3 U {cd} a hamiltonian path with endpoints a and b and containing the edge cd. Al
Let G be a group generated by X. A Cayley graph ouer G is defined as a graph G(X) whose vertex set is G and whose edge set consists of all unordered pairs [a, b] with a, b E G and am'b E X U X-', where X-t denotes the set (x-t ( .x E X}. When X is a minimal generating set or each element of X is of
## Abstract In this paper, we show that if __G__ is a 3βedgeβconnected graph with $S \subseteq V(G)$ and $|S| \le 12$, then either __G__ has an Eulerian subgraph __H__ such that $S \subseteq V(H)$, or __G__ can be contracted to the Petersen graph in such a way that the preimage of each vertex of th
## Abstract A constructive characterization of minimally 2βedge connected graphs, similar to those of Dirac for minimally 2βconnected graphs is given.
## Abstract Let Ξ³(__G__) be the domination number of graph __G__, thus a graph __G__ is __k__βedgeβcritical if Ξ³ (__G__)β=βk, and for every nonadjacent pair of vertices __u__ and Ο , Ξ³(__G__β+β__u__Ο )β=βkβ1. In Chapter 16 of the book βDomination in GraphsβAdvanced Topics,β D. Sumner cites a conjectu