A Hamiltonian path or traceable path is a path that visits each vertex of the graph exactly once. A graph that contains a Hamiltonian path is called a traceable graph. A graph is Hamiltonian-connected if for every pair of vertices … 展开

Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to a Hamiltonian cycle only if its endpoints are adjacent. 展开

An algebraic representation of the Hamiltonian cycles of a given weighted digraph (whose arcs are assigned weights from a certain ground field) is the Hamiltonian cycle polynomial of its weighted adjacency matrix defined as the sum of the products of … 展开

• Weisstein, Eric W. "Hamiltonian Cycle". MathWorld.
• Euler tour and Hamilton cycles 展开

• A complete graph with more than two vertices is Hamiltonian
• Every cycle graph is Hamiltonian
• Every tournament has an odd number of Hamiltonian paths (Rédei 1934)
• Every platonic solid, considered as a graph, is Hamiltonian 展开

The best vertex degree characterization of Hamiltonian graphs was provided in 1972 by the Bondy–Chvátal theorem, which generalizes earlier results by 展开

• Barnette's conjecture, an open problem on Hamiltonicity of cubic bipartite polyhedral graphs
• Eulerian path, a path through all edges in a graph
• Fleischner's theorem, on Hamiltonian squares of graphs 展开