On Finding Lekkerkerker-Boland Subgraphs

TL;DR

This paper presents linear-time algorithms for identifying minimal forbidden subgraphs and submatrices related to interval graphs and the consecutive-ones property, improving detection efficiency.

Contribution

It introduces efficient algorithms for finding minimal forbidden structures in graphs and matrices, extending prior characterizations to practical linear-time solutions.

Findings

Linear-time algorithm for Lekkerkerker-Boland subgraphs

Linear-time algorithm for minimal forbidden submatrices

Enhanced detection of non-interval graphs and matrices

Abstract

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