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Lengths of cycles in halin graphs
Author(s) -
Bondy J. A.,
Lovász L.
Publication year - 1985
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190090311
Subject(s) - combinatorics , mathematics , vertex (graph theory) , graph , discrete mathematics , degree (music) , physics , acoustics
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.