Dominating sets and hamiltonicity inK1,3-free graphs
β Scribed by A. A. Ageev
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1994
- Tongue
- English
- Weight
- 271 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0037-4466
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
## Abstract In this paper, we investigate the Hamiltonicity of __K__~1,r~βfree graphs with some degree conditions. In particular, let __G__ be a __k__βconnected grph of order __n__β§3 which is __K__~1,4~βfree. If magnified image for every independent set {__v__~0~, __v__~1~, β¦, __v__~k~} then __G__
Using Ryja c ek's closure, we prove that any 3-connected claw-free graph of order & and minimum degree $ &+38 10 is hamiltonian. This improves a theorem of Kuipers and Veldman who got the same result with the stronger hypotheses $ &+29 8 and & sufficiently large and nearly proves their conjecture sa