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We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(G), and construct a tree with at least (n−x(G)+4)/3… (More)

The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum diierence between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every graph, with equality for certain caterpillars. We obtain sharp or nearly-sharp bounds on the change in edge-bandwidth… (More)