Conservative weightings and ear-decompositions of graphs
Conservative weightings and ear-decompositions of graphs
复制标题
图的保守权重和耳朵分解
DOI：
10.1007/bf01202790
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发表时间：
1990
期刊：
影响因子：
1.1
通讯作者：
A. Frank
中科院分区：
文献类型：
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作者：
A. Frank
如果|c∩j|≤| c |/2，每个电路的ED Gragrg =（V，E）的边缘被称为Ajoin。 Min-Max公式的最大基数μ的g。参数我们介绍了一个新的分解，很有趣自有的清酒，其构建块是关键因素图和匹配覆盖的两分图。证明依赖于加莱 - 埃德蒙兹结构定理，并产生多项式时间算法来构建所讨论的最佳。
A subsetJ of edges of a connected undirected graphG=(V, E) is called ajoin if |C∩J|≤|C|/2 for every circuitC ofG. Answering a question of P. Solé and Th. Zaslavsky, we derive a min-max formula for the maximum cardinality μ of a joint ofG. Namely, μ=(φ+|V|−1)/2 where φ denotes the minimum number of edges whose contraction leaves a factor-critical graph.To study these parameters we introduce a new decomposition ofG, interesting for its own sake, whose building blocks are factor-critical graphs and matching-covered bipartite graphs. We prove that the length of such a decomposition is always φ and show how an optimal join can be constructed as the union of perfect matchings in the building blocks. The proof relies on the Gallai-Edmonds structure theorem and gives rise to a polynomial time algorithm to construct the optima in question.