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...
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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