Linear-Time Algorithms for Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs

Tucker characterized the minimal forbidden submatrices of binary matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find such a minimal one in any binary matrix that does not have the consecutive-ones property. Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm to find such a minimal one in any graph that is not an interval graph.