TL;DR
This paper introduces a new property of Hamilton graphs, providing a necessary and sufficient condition based on subgraph connectivity related to the cycle structure of the graph.
Contribution
It defines new subgraph concepts and characterizes Hamiltonicity through subgraph connectivity, advancing understanding of Hamilton cycle conditions.
Findings
New subgraph definitions related to Hamiltonicity
Necessary and sufficient condition based on subgraph connectivity
Characterization of Hamilton graphs via cycle structure
Abstract
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Interconnection Networks and Systems · Advanced Graph Theory Research