Bandwidth and density for block graphs
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The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special class of block graphs (graphs in which every block is a clique), namely those where deleting the vertices of degree one produces a path of cliques. The result is best possible in various ways. Furthermore, for two classes of graphs that are ``almost'' caterpillars, the bandwidth problem is NP-complete.
14 pages, 9 included figures. Note: figures did not appear in original upload; resubmission corrects this
14 pages, 9 included figures. Note: figures did not appear in original upload; resubmission corrects this