Heavy cycles in 2-connected triangle-free weighted graphs |
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Authors: | Xue Zheng Lv Pei Wang |
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Institution: | 1. Department of Mathematics, Renmin University of China, Beijing 100872, P. R. China;
2. Department of Mathematics and Physics, China University of Petroleum, Beijing 102249, P. R. China |
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Abstract: | A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw(v). The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a 2-connected triangle-free weighted graph of even size such that dw(u) + dw(v) ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V (G), then G contains a cycle of weight at least 2d. |
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Keywords: | Heavy cycles triangle-free graphs weighted graphs |
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