The binding number of a graph and its circuits |
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Authors: | Shi Ronghua |
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Affiliation: | (1) Qinghai Normal University, Qinghai, China |
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Abstract: | In this paper we prove the following main results:Theorem A. If bind (G) 3/2, thenG–u has a Hamiltonian circuit for every vertexu of graphGi, unlessG belongs either to two classesH1 andH2 of graphs or to some smaller order graphs with |V(G)| 17.Theorem B. If bind (G) 3/2 and the maximum degree (G)>(n–1)/2, |V(G)|=n>17, thenG is pancyclic (i.e., it contains a circuit of every lengthm, 3 m |V(G)|). |
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