一般图的哈密顿图的研究进展  

A Survey of the Advances of Hamiltonicity on Simple Graphs

作　　者：陈德钦[1] 赵克文[1] 

机构地区：[1]琼州大学数学系,三亚572022

出　　处：《数学理论与应用》2011年第2期92-99,共8页Mathematical Theory and Applications

摘　　要：1991年刘振宏和李明楚在南京大学召开的首届哈密顿图研讨会的综述文章中说"要给出一个一般图具有哈密顿圈的充分条件是一件非常不容易的事"。因哈密顿图是含哈密顿圈的图类,如此哈密顿图主要有六个方向:哈密顿圈、哈密顿连通、泛圈图、点泛圈图、泛连通图、最短路径泛圈图。本文中,我们就给出一般图的这些领域新进展的小综述。In 1991 Liu and Li stated that ＂It is a very difficult problem to give a sufficient condition for Hamihonian cycle without forbidden subgraphs＂. A graph is said to be Hamihonian graph if it contains a Hamihonian cycle. There are several classes of well - known Hamiltonian graphs such as Hamihonian cycles, Hamihonian - connected, pan- cyclic, vertex - pancyclic, panconnected and Geodesic - pancyclic et al. In this paper we mainly state some recent advances in the several topics of Hamihonian graphs on simple graphs.

关 键 词：哈密顿圈 哈密顿连通图 泛圈图 点泛圈图 泛连通图 充分条件 

分 类 号：O157.5[理学—数学]