On maximum spanning tree-packable graphs and uncoverings-by-bases
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چکیده
We define an uncovering-by-bases for a connected graph G to be a collection U of spanning trees for G such that any t-subset of edges of G is disjoint from at least one tree in U , where t is some integer strictly less than the edge connectivity of G. We construct examples of these for some infinite families of graphs. We then characterize maximum spanning tree-packable graphs, i.e. those graphs G for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees in G. These graphs are of interest as they have uncoverings-by-bases of the least possible size while t is maximal. We also discuss a potential application to network reliability.
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تاریخ انتشار 2009