Hamiltonian properties of domination-critical graphs
β Scribed by Ewa Wojcicka
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 445 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
In this paper we show that every connected, 3βΞ³βcritical graph on more than 6 vertices has a Hamiltonian path.
π SIMILAR VOLUMES
We show that for each k L 4 there exists a connected k-domination critical graph with independent domination number exceeding k, thus disproving a conjecture of Sumner and Blitch ( J Cornbinatorial Theory B 34 (19831, 65-76) in all cases except k = 3.
## Abstract A graph __G__ is 3βdomination critical if its domination number Ξ³ is 3 and the addition of any edge decreases Ξ³ by 1. Let __G__ be a 3βconnected 3βdomination critical graph of order __n__. In this paper, we show that there is a path of length at least __n__β2 between any two distinct ve
Let Ξ΄, Ξ³, i and Ξ± be respectively the minimum degree, the domination number, the independent domination number and the independence number of a graph G. The graph G is 3-Ξ³-critical if Ξ³ = 3 and the addition of any edge decreases Ξ³ by 1. It was conjectured that any connected 3-Ξ³-critical graph satisf