Research On Hamilton Cycle Problem Of Graphs And Hypergraphs

In this paper,we mainly research on Hamilton cycle problem of graphs and hypergraphs,which is divided into the Hamiltonian cycle problem of graph and the Hamiltonian cycle problem of hypergraph.In the introduction part,the related research background and general situation and the defination of each chapter will be given.The Hamiltonian cycle problem of graph part is divided into two chapters,mainly discuss the number and structure of Hamiltonian cycle of graph in specific conditions.Hamiltonian cycle problem of graph is mainly put forward by the Lucas who research the problems and the promote problems of couples around the round table respectively.Mainly includes the couple along a straight line table problem;Couple along both lines table problem;Couple along three lines table,etc.In this section,the collection of recursive method the determinant method,sequence method has been mainly applied.In each section give Hamiltonian cycle structure and counting under specific conditions.In the Hamiltonian cycle problem of the hypergraph section,mainly discusses the Hamiltonian cycle problem of ?-repeated 3- consistent hypergraph under the 3(?)m condition,including the existence of hamiltonian decomposition,the structure of the Hamiltonian cycle.Then the existence of the hamilton cyle decomposition problem of ?-repeated 3- uniform hypergraph is solved.Finally,the existence of Hamiltonian cycle decomposition and structural problems of ?-repeated r-uniform hypergraph are discussed under the r(?)mr-1,?=r condition.In this section,mainly use the relationship between the ring Zrm and vertex set of hypergraph,then according the difference and extended difference method to research on the corresponding sequence.