Hamiltonian degree conditions which imply a graph is pancyclic
Let G be a finite undirected graph without loops or multiple edges. Various sufficient degree conditions for such graphs to be Hamiltonian have been given by Chvatál, Fan and Bondy (propositions 1, 2, 3). In this paper it is shown that exactly each of the conditions in these propositions imply still more about the cycle structure of G. A n-vertex graph is said to be pancyclic if it contains a l-cycle for every l such that holds \(3\leq l\leq n.\) And by three main theorems it is proved that G is not only Hamiltonian but even either pancyclic, bipartite or a member of a certain family of exceptions. Going out from the propositions 1, 2, 3 the theorems are proved by using four interesting lemmas, the third of them especially describes further important properties of n-vertex graphs with Hamiltonian cycle.
special cyclic structure of Hamiltonian graphs
scientific article; zbMATH DE number 4144021