Bandwidth and density for block graphs

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.Comment: 14 pages, 9 included figures. Note: figures did not appear in original upload; resubmission corrects thi

Maximal outerplanar graphs with perfect faceindependent vertex covers

AbstractA subset W of vertices of a plane graph is said to be a perfect face-independent vertex cover (FIVC) if and only if each face-boundary contains exactly one vertex from W. We characterize maximal outerplanar graphs admitting plane embeddings with perfect FIVCs