The Forbidden Subgraphs For Hamiltonian Graph

Forbidden subgraphs are special kinds of figures in graph theory and play a important role in Hamiltonian graphs.Theory of cycles and paths is an important branch of graph theory.Hamilton properties of graphs is a di cult topic in graph theory.This paper surveys the past and recent research situations.This paper introduces some important concepts related to the forbidden sub-graphs,conclusions and the proof of a new result.The main content is as follows.The first chapter introduces the basic knowledge and Hamilton properties of graphs.The second chapter introduces the Hamilton properties of claw-free graphs in the large degree conditions in detail,and the large degree conditions mainly include the conditions of minimum degree,Fan-type,independent set,Ore-type.The third chapter introduces the Hamilton properties with the connectivity condition.In this chapter we will extend the connectivity’s concept and give the concepts of locally connected,N₂-connected and the results in these new conditions.The fourth chapter introduces the Hamilton properties of multiple forbidden subgraphs.The fifth chapter introduces the Hamilton properties of some graphs which are larger than the claw-free graphs,such as the quasi-claw-free graphs,al-most claw-free graphs and heavy-claw graphs.In the sixth chapter we give a Hamilton graph in a neighborhood intersection condition and a simple proof.