Recognition and characterization of unit interval graphs with integer endpoints

We study those unit interval graphs having a model with intervals of integer endpoints and prescribed length. We present a structural result for this graph subclass which leads to a quadratic-time recognition algorithm, giving as positive certificate a model of minimum total length and as negative certificate a forbidden induced subgraph. We also present a quadratic-time algorithm to build, given a unit interval graph, a unit interval model with integer endpoints for which the interval length is as minimum as possible.Fil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Chile; Chile. Universidad de Buenos Aires; ArgentinaFil: Fernández Slezak, F.. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Grippo, L.N.. Universidad Nacional de General Sarmiento; ArgentinaFil: Oliveira, F.de S.. Universidade do Estado de Rio do Janeiro; BrasilFil: Szwarcfiter, Jayme L.. Universidade do Estado de Rio do Janeiro; Brasil. Universidade Federal do Rio de Janeiro; Brasi

Recognition and characterization of unit interval graphs with integer endpoints

We study those unit interval graphs having a model with intervals of integer endpoints and prescribed length. We present a structural result for this graph subclass which leads to a quadratic-time recognition algorithm, giving as positive certificate a model of minimum total length and as negative certificate a forbidden induced subgraph. We also present a quadratic-time algorithm to build, given a unit interval graph, a unit interval model with integer endpoints for which the interval length is as minimum as possible. (C) 2017 Elsevier B.V. All rights reserved.Complex Engineering Systems Institute, Chile CONICYT - PIA - FB0816; ICM P-05-004-F ANPCyT PICT-2012-1324 UBACyT (Argentina) 20020130100808BA PIO CONICET UNGS-144-20140100011-CO FAPERJ CNPq CAPE