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Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

Tutte's (46-vertex) graph is a cubic nonhamiltonian graph contructed by Tutte (1946) as a counterexample to Tait's Hamiltonian graph conjecture by using three copies ...

A theory of Hamiltonian cycles.

The Faulkner-Younger graphs (Faulkner and Younger 1974) are the cubic polyhedral nonhamiltonian graphs on 42 and 44 vertices illustrated above that are counterexamples to ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

A cubic polyhedral graph is a graph that is both cubic and polyhedral. The numbers of cubical polyhedral graphs on n=2, 4, ... nodes are 0, 1, 1, 2, 5, 14, 50, 233, 1249, ... ...

Tait's Hamiltonian graph conjecture asserted that every cubic polyhedral graph is Hamiltonian. It was proposed by Tait in 1880 and refuted by Tutte (1946) with a ...

A graph cycle.