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On hamiltonicity of P3-dominated graphs

Broersma, H.J.; Vumar, E.


H.J. Broersma

E. Vumar


We introduce a new class of graphs which we call P₃-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P₃-dominated graph. We prove that G is hamiltonian if α(G²) ≤ κ(G), with two exceptions: K₂,₃ and K₁,₁,₃. We also prove that G is hamiltonian, if G is 3-connected and |V(G)| ≤ 5δ(G) − 5. These results extend known results on (quasi-)claw-free graphs.


Broersma, H., & Vumar, E. (2009). On hamiltonicity of P3-dominated graphs. Mathematical Methods of Operations Research, 69(2), 297-306.

Journal Article Type Article
Publication Date May 1, 2009
Deposit Date Mar 1, 2010
Journal Mathematical Methods of Operations Research
Print ISSN 1432-2994
Electronic ISSN 1432-5217
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 69
Issue 2
Pages 297-306
Keywords Claw-free graph, Quasi-claw-free graph, Hamiltonian cycle, P₃-dominated graph.