Broersma, H. J. and Vumar, E. (2009) 'On hamiltonicity of P₃-dominated graphs.', Mathematical methods of operations research., 69 (2). pp. 297-306.
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.
|Keywords:||Claw-free graph, Quasi-claw-free graph, Hamiltonian cycle, P₃-dominated graph.|
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|Publisher Web site:||http://dx.doi.org/10.1007/s00186-008-0260-7|
|Record Created:||01 Mar 2010 13:05|
|Last Modified:||08 Dec 2010 11:57|
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