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pancyclic graph
In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from three up to the number of vertices in the graph.〔.〕 Pancyclic graphs are a generalization of Hamiltonian graphs, graphs which have a cycle of the maximum possible length.
==Definitions==
An ''n''-vertex graph ''G'' is pancyclic if, for every ''k'' in the range , ''G'' contains a cycle of length ''k''.〔 It is node-pancyclic or vertex-pancyclic if, for every vertex ''v'' and every ''k'' in the same range, it contains a cycle of length ''k'' that contains ''v''.〔.〕 Similarly, it is edge-pancyclic if, for every edge ''e'' and every ''k'' in the same range, it contains a cycle of length ''k'' that contains ''e''.〔
A bipartite graph cannot be pancyclic, because it does not contain any odd-length cycles, but it is said to be bipancyclic if it contains cycles of all even lengths from 4 to ''n''.〔.〕
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