The minimum spanning tree and duality in graphs
نویسنده
چکیده
Several algorithms for the minimum spanning tree are known. The Blue-red algorithm is a generic algorithm in this field. A new proof for this algorithm is presented, based upon the duality of circuits and cuts in a graph. The Blue-red algorithm is genetic, because the other algorithms can be regarded as special instances. This is shown using the same duality.
منابع مشابه
Counting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملA Metaheuristic Algorithm for the Minimum Routing Cost Spanning Tree Problem
The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start ...
متن کاملA Stock Market Filtering Model Based on Minimum Spanning Tree in Financial Networks
There have been several efforts in the literature to extract as much information as possible from the financial networks. Most of the research has been concerned about the hierarchical structures, clustering, topology and also the behavior of the market network; but not a notable work on the network filtration exists. This paper proposes a stock market filtering model using the correlation - ba...
متن کاملSpanning tree congestion: duality and isoperimetry. With an application to multipartite graphs
In this paper we (1) Describe two approaches to estimates of the spanning tree congestion from below; (2) Use the isoperimetric approach to find the exact value of the spanning tree congestion of complete multipartite graphs; (3) Present a proof of the isoperimetric result of Piliposyan-Muradyan for complete multipartite graphs.
متن کاملalgorithms for parametric minimum spanning tree problems on planar graphs ’
A linear-time algorithm for the minimum-ratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators.
متن کامل