A graph G is N 2 -locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryja Β΄c Λek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro
Sufficient condition for Hamiltonicity of N2-locally connected claw-free graphs
β Scribed by Halina Bielak
- Book ID
- 108316388
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 89 KB
- Volume
- 213
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __cl__(__G__) denote RyjΓ‘Δek's closure of a clawβfree graph __G__. In this article, we prove the following result. Let __G__ be a 4βconnected clawβfree graph. Assume that __G__[__N__~__G__~(__T__)] is cyclically 3βconnected if __T__ is a maximal __K__~3~ in __G__ which is also maxim
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,