J4 ›› 2009, Vol. 44 ›› Issue (10): 21-25.

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A degree condition for graphs to have Hamiltonian (g,f)-factors

 WANG Chao   

  1. 1. School of Mathematics and Statistics, Shandong University at Weihai, Weihai264200, Shandong, China;2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2009-04-20 Online:2009-10-16 Published:2009-12-07

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Abstract:

Let G be a 2 connected graph of order n, and let a and b be integers such that 2≤a＜b, and let g(x) and f(x) be two nonnegative integer valued  functions defined on V(G) such that a≤g(x)＜f(x)≤b for each x∈V(G). It is proved that G has a Hamiltonian (g,f) factor if the minimum degree of G satisfies the following conditions,δ(G)≥[(b-1)2-(a-1)(b-a)]/(a-1)〖SX)〗,[n＞(a+b-3)(a+b-2)]/(a-1), and max｛dG(x) ,dG(y) ｝≥(b-1)n/(a+b-2) for any two nonadjacent vertices x and y in G.

Key words: graph; (g,f)-factor; Hamiltonian (g,f)-factor

CLC Number: 

  • O157.5
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