Lengths of cycles in halin graphs |
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Authors: | J A Bondy L Lovsz |
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Institution: | J. A. Bondy,L. Lovász |
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Abstract: | A Halin graph is a plane graph H = T U C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the endvertices of T in the cyclic order determined by the embedding of T. We prove that such a graph on n vertices contains cycles of all lengths l, 3 ≤ l n, except, possibly, for one even value m of l. We prove also that if the tree T contains no vertex of degree three then G is pancyclic. |
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