Their existence can be guaranteed by meeting either the conditions of Ore's theorem or of Bondy and Chvatal's theorem, and the Smith Network Theorem gives their number as either 0 or even if each vertex posesses three edges.
All of them satisfy the Grinberg formula and one of these is possessed by every Platonic solid. Their existence can be guaranteed by meeting either the conditions of Ore's theorem or of Bondy and Chvatal's theorem, and the Smith Network Theorem gives their number as either 0 or even if each vertex posesses three edges. Dirac's theorem, generalized by Posa, states that one of these exists for every graph with 3 or more vertices and a minimum degree of at least n over 2, and one example of a problem that involves finding one of these is the traveling salesman problem. Consisting of a path through a graph that visits every vertex exactly once and returns to the starting point, for ten points, identify this graph cycle named for the 19th century Irish mathematician who invented quatternions.
All of them satisfy the Grinberg formula and one of these is possessed by every Platonic solid.
{Hamiltonian} cycle