There have been a number of results dealing with Hamiltonian properties in powers of graphs. In this paper we show that the square and the total graph of a K,,,-free graph are vertex pancyclic. We then discuss some of the relationships between connectivity and Hamiltonian properties in K,.3-free gra
Some recent results in hamiltonian graphs
β Scribed by L. Lesniak-Foster
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 505 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
A variety of recent developments in hamiltonian theory are reviewed. In particular, several sufficient conditions for a graph to be hamiltonian, certain hamiltonian properties of line graphs, and various hamiltonian properties of powers of graphs are discussed. Furthermore, the concept of an nβdistant hamiltonian graph is introduced and several theorems involving this special class of hamiltonian graphs are presented.
π SIMILAR VOLUMES
Let k β₯ 2 be an integer. A k-factor F of a graph G is called a hamiltonian k-factor if F contains a hamiltonian cycle. In this paper, we shall prove that if G is a graph of order n with k β₯ 2, n β₯ 8k -4, kn even and Ξ΄(G) β₯ n/2, then G has a hamiltonian k-factor.
## 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
## Abstract A graph __G__ of order at least 2__n__+2 is said to be __n__βextendable if __G__ has a perfect matching and every set of __n__ independent edges extends to a perfect matching in __G__. We prove that every pair of nonadjacent vertices __x__ and __y__ in a connected __n__βextendable graph