It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph.In spite of the difficulty in proving this conjecture,we show that almost all Cayley graphs are hamiltonian.That is,as t...It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph.In spite of the difficulty in proving this conjecture,we show that almost all Cayley graphs are hamiltonian.That is,as the order n of a group G approaches infinity,the ratio of the number of hamiltonian Cayley graphs of G to the total number of Cayley graphs of G approaches 1.展开更多
基金Supported by the National Natural Science Foundation of China,Xinjiang Educational Committee and Xinjiang University.
文摘It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph.In spite of the difficulty in proving this conjecture,we show that almost all Cayley graphs are hamiltonian.That is,as the order n of a group G approaches infinity,the ratio of the number of hamiltonian Cayley graphs of G to the total number of Cayley graphs of G approaches 1.
