One sufficient condition for hamiltonian graphs
β Scribed by Guantao Chen
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 220 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let G be a 2βconnected graph of order n. We show that if
for each pair of nonadjacent vertices x,y β V(G), then G is Hamiltonian.
π SIMILAR VOLUMES
The total chromatic number Ο T (G) of graph G is the least number of colors assigned to V (G) βͺ E(G) such that no adjacent or incident elements receive the same color. In this article, we give a sufficient condition for a bipartite graph G to have Ο T (G) = β(G) + 1.
We describe a new type of sufficient condition for a digraph to be Hamiltonian. Conditions of this type combine local structure of the digraph with conditions on the degrees of nonadjacent vertices. The main difference from earlier conditions is that we do not require a degree condition on all pairs
## Abstract For a positive integer __k__, a graph __G__ is __kβordered hamiltonian__ if for every ordered sequence of __k__ vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. It is shown that if __G__ is a graph of order __n__ with 3 β€ __k__ β€ __n
We prove the following conjecture of Broersma and Veldman: A connected, locally k-connected K,,-free graph is k-hamiltonian if and only if it is (k + 2)-connected ( k L 1). We use [ 11 for basic terminology and notation, and consider simple graphs only. Let G be a graph. By V(G) and E(G) we denote,