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  2. Hamiltonian path - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_path

    A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices. A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph.

  3. Petersen graph - Wikipedia

    en.wikipedia.org/wiki/Petersen_graph

    The Petersen graph is hypo-Hamiltonian: by deleting any vertex, such as the center vertex in the drawing, the remaining graph is Hamiltonian. This drawing with order-3 symmetry is the one given by Kempe (1886). The Petersen graph has a Hamiltonian path but no Hamiltonian cycle. It is the smallest bridgeless cubic graph with no Hamiltonian cycle.

  4. File:Hamiltonian platonic graphs.svg - Wikipedia

    en.wikipedia.org/wiki/File:Hamiltonian_platonic...

    Hamiltonian platonic graphs: Image title: Orthographic projections and planar graphs of Hamiltonian cycles of the vertices of the five Platonic solids by CMG Lee. Only the octahedron has an Eulerian path, made by extending the Hamiltonian path with the dotted path. Width: 100%: Height: 100%

  5. Hamiltonian path problem - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_path_problem

    A verifier algorithm for Hamiltonian path will take as input a graph G, starting vertex s, and ending vertex t. Additionally, verifiers require a potential solution known as a certificate, c. For the Hamiltonian Path problem, c would consist of a string of vertices where the first vertex is the start of the proposed path and the last is the end ...

  6. Tournament (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Tournament_(graph_theory)

    The Hamiltonian paths are in one-to-one correspondence with the minimal feedback arc sets of the tournament. [3] Rédei's theorem is the special case for complete graphs of the Gallai–Hasse–Roy–Vitaver theorem , relating the lengths of paths in orientations of graphs to the chromatic number of these graphs.

  7. Category:Hamiltonian paths and cycles - Wikipedia

    en.wikipedia.org/wiki/Category:Hamiltonian_paths...

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  9. Ore's theorem - Wikipedia

    en.wikipedia.org/wiki/Ore's_theorem

    Illustration for the proof of Ore's theorem. In a graph with the Hamiltonian path v 1...v n but no Hamiltonian cycle, at most one of the two edges v 1 v i and v i − 1 v n (shown as blue dashed curves) can exist. For, if they both exist, then adding them to the path and removing the (red) edge v i − 1 v i would produce a Hamiltonian cycle.