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.
Hamiltonian-laceability of star graphs
β Scribed by Sun-Yuan Hsieh; Gen-Huey Chen; Chin-Wen Ho
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 147 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine
A hamiltonian graph G of order n is k-ordered, 2 β€ k β€ n, if for every sequence v 1 , v 2 , . . . , v k of k distinct vertices of G, there exists a hamiltonian cycle that encounters v 1 , v 2 , . . . , v k in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be h
We give a simple proof that the obvious necessary conditions for a graph to contain the k th power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We wi
We prove that every 18-tough chordal graph has a Hamiltonian cycle.
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In answer to a question of ErdΕs, we show that a Hamiltonian weakly-pancyclic graph of order n can have girth as large as about 2 n/ log n. In contrast to this, we show that the existence of