On neighborhood condition for graphs to have [a,b]-factors |
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| Authors: | Jianxiang Li |
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| Institution: | Department of Mathematics of Xiangtan Polytechnic University, Xiangtan, Hunan 411201, People's Republic of China |
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| Abstract: | Let G be a graph of order n, and let a and b be integers such that 1 a<b. Let δ(G) be the minimum degree of G. Then we prove that if δ(G) (k?1)a, n(a+b)(k(a+b)?2)/b, and |NG(x1) NG(x2) NG(xk)|an/(a+b) for any independent subset {x1,x2,…,xk} of V(G), where k2, then G has an a,b]-factor. This result is best possible in some sense. |
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| Keywords: | Graph Factor [a b]-Factor Neighborhood |
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