Abstract
The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced. A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgraph of it. In this paper, a good characterization of w-balanced weighted graphs is given. Applying this characterization, many large w-balanced weighted graphs are formed by combining smaller ones. In the case where a graph is not w-balanced, a polynomial-time algorithm to find a subgraph of maximum w-density is proposed. It is shown that the w-density theory is closely related to the study of SEW (G,w) games.
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Supported by the National Natural Science Foundation of China (10101021).
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Shenggui, Z., Hao, S. & Xueliang, L. w-Density and w-balanced property of weighted graphs. Appl. Math. Chin. Univ. 17, 355–364 (2002). https://doi.org/10.1007/s11766-002-0015-9
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DOI: https://doi.org/10.1007/s11766-002-0015-9