Spanning Tree
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In the mathematics|mathematical field of graph theory, a spanning tree T of a connected graph|connected, undirected graph G is a tree (graph theory)|tree composed of all the Vertex (graph theory)|vertices and some (or perhaps all) of the Edge (graph theory)|edges of G. Informally, a spanning tree of G is a selection of edges of G that form a tree spanning every vertex. That is, every vertex lies in the tree, but no cycle (graph theory)|cycles (or loops) are formed. On the other hand, every bridge (graph theory)|bridge of G must belong to T. A spanning tree of a connected graph G can also be defined as a maximal set of edges of G that contains no cycle, or as a minimal set of edges that connect all vertices. In certain fields of graph theory it is often useful to find a minimum spanning tree of a weighted graph. Other optimization problems on spanning trees have also been studied, including the maximum spanning tree, the minimum tree that spans at least k vertices, the minimum spanning...
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Lower Bound    
Planar Graph    
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