Bandwidth and topological bandwidth of graphs with few P4ʹs Original Research Article

We give a polynomial time algorithm to compute the bandwidth of a (q,q−4)-graph for each constant q. We show also that the bandwidth and topological bandwidth of P4-sparse graphs are equal. Let H be a subdivision of a graph G with a minimal number of vertices such that the bandwidth of H equals the topological bandwidth of G. We show that the number of vertices of H is O(n3), where n is the number of vertices in G, and thus the topological bandwidth of a graph of constant size can be computed in constant time.