图的哈密尔顿性的研究

哈密尔顿相关问题的研究一直是许多图论研究者感兴趣的课题之一。这方面研究众多，出现了许多经典的结论。本项目主要研究(1)禁用子图的哈密尔顿相关问题。如果图G中不包含任何同构于F_i{1≤i≤ k}的导出子图，那么称图G是F_1,F_2,……,F_k-禁用子图。本项目拟刻画R,S图，使得3-连通{R,S}-禁用子图是哈密尔顿连通的(或泛圈的)；(2){R,S}-o_i-heavy图的哈密尔顿相关问题(这里i=0,1)。 设G的顶点数为n且G'是G的一个导出子图，若G'中存在两个不相邻的顶点在G中的度数至少为n+i，则称G'是o_i-heavy(这里i=0,1)。本项目拟刻画图R,S，使连通{R,S}-o_i-heavy图有一个生成迹，这里i=0,1。(3)具有局部连通顶点的图的哈密尔顿相关问题。本项目拟刻画刻画H-禁用子，使N^3-局部连通H-禁用子图且最小度大于等于3是超欧拉的。

The research of some problems about the Hamiltonicity has been one of many graphtheory reseachers interested in. Research in this field is multitudinous and there are many classical results. In this project, we systematically study (1) Hamiltonian related problems of forbidden subgraphs. If graph G does not contain any induced subgraphs isomorphic to F_i{1≤i≤ k}, then graph G is calledF_1,F_2,……,F_k-forbidden subgraphs. In this paper, we intend to characterize the graphs R, S so that 3-connected {R, S} - forbidden subgraphs are Hamiltonian connected (or pancyclic); (2) Hamiltonian related problems of {R, S} -o-heavy graphs (where i= 0,1). Let |V(G)| = n and G 'be an induce subgraph of G, If there are two non adjacent vertices in G whose degree is at least n + i, then G' is o_i-heavy (where I = 0,1). In this project, we want to characterize graph R, S so that the connected {R, s} - O _ i-heavy graph has a spanning trace, where i = 0,1. (3)Hamiltonian related problems of graphs with locally connected vertices. In this project, we intend to characterize and characterize H-forbidden subgraphs so that N^ 3-locally connected H-forbidden subgraphs with a minimum degree greater than or equal to 3 are hypereulerian.