On hamiltonicity of P 3 -dominated graphs

H. Broersma () and E. Vumar ()

Mathematical Methods of Operations Research, 2009, vol. 69, issue 2, 297-306

Abstract: We introduce a new class of graphs which we call P 3 -dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P 3 -dominated graph. We prove that G is hamiltonian if α(G 2 ) ≤ κ(G), with two exceptions: K 2,3 and K 1,1,3 . 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. Copyright Springer-Verlag 2009

Keywords: Claw-free graph; Quasi-claw-free graph; Hamiltonian cycle; P 3 -dominated graph; 05C45; 05C38 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s00186-008-0260-7

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