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	FAN TYPE CONDITION AND CHARACTERIZATION OF HAMILTONIAN GRAPHS
	Chao, Kewen ; Song, Chunwei ; Zhang, Ping
	2014
关键词	Hamiltonian Fan condition Benhocine-Wojda condition Ore condition
英文摘要	Let G be a simple graph of order n >= 3. Ore's classical theorem states that if d(x) + d(y) >= n for each pair of nonadjacent vertices x, y is an element of V (G), then G is Hamiltonian (Amer. Math. Monthly 67 (1960), 55). In 1984, Fan proved that if G is 2-connected and max{d(x), d(y)} >= n/2 for each pair of vertices x, y with distance 2, then G is Hamiltonian. Fan's result is a significant improvement to Ore's theorem, and the condition stated is called Fan's condition. Then in 1987, Benhocine and Wojda showed that if G is a 2-connected graph with independence number alpha(G) <= n/2, and max{d(x), d(y)} >= n-1/2 for each pair of vertices x, y with distance 2, then G is Hamiltonian with some exceptions: either G is Hamiltonian or G belongs to one of two classes of well characterized graphs. In 2007, Li et al. removed the independence restriction, but they also reversed the Fan type bigger degree lower bound condition to the stronger Ore type degree sum requirement. In our present work, we drop the independence restriction while keeping Benhocine and Wojda's relaxed Fan type condition to prove that if G is 2-connected and max{d(x), d(y)} >= n-1/2 for each pair of vertices x, y with distance 2, then either G is Hamiltonian or G is among certain classes of well characterized graphs. This extends previous results in the literature.; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; kewen@bxemail.com; csong@math.pku.edu.cn; ping.zhang@wmich.edu; 7; 2303-2311; 142
语种	英语
出处	SCI
出版者	proceedings of the american mathematical society
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/392848]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chao, Kewen,Song, Chunwei,Zhang, Ping. FAN TYPE CONDITION AND CHARACTERIZATION OF HAMILTONIAN GRAPHS. 2014-01-01.

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