Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical study of graph theory, a pancyclic graph is a directed 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. A tournament is a directed graph with one directed edge between each pair of vertices. Intuitively, a tournament can be used to model a round-robin sports competition, by drawing an edge from the winner to the loser of each game in the competition. A tournament is called strongly connected or strong if and only if it cannot be partitioned into two subsets L and W of losers and winners, such that every competitor in W beats every competitor in L. Every strong tournament is pancyclic and node-pancyclic.

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