On Hamiltonicity of 3-Connected Claw-Free Graphs

On Hamiltonicity of 3-Connected Claw-Free Graphs

Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005 ) showed that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle...

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Veröffentlicht in:Graphs and combinatorics 2014-09, Vol.30 (5), p.1261-1269
Hauptverfasser: Tian, Runli, Xiong, Liming, Niu, Zhaohong
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Combinatorics
Disengaging
Engineering Design
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
Triangles
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Zusammenfassung:Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005 ) showed that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of G is Hamiltonian. It is best possible in some sense.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-013-1343-7