1 research outputs found
A New Property of Hamilton Graphs
A Hamilton cycle is a cycle containing every vertex of a graph. A graph is
called Hamiltonian if it contains a Hamilton cycle. The Hamilton cycle problem
is to find the sufficient and necessary condition that a graph is Hamiltonian.
In this paper, we give out some new kind of definitions of the subgraphs and
determine the Hamiltoncity of edges according to the existence of the subgraphs
in a graph, and then obtain a new property of Hamilton graphs as being a
necessary and sufficient condition characterized in the connectivity of the
subgraph that induced from the cycle structure of a given graph