On counting interval lengths of interval graphs

Authors:
Márcia R. Cerioli;Fabiano de S. Oliveira;Jayme L. Szwarcfiter
Affiliations:
COPPE/Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21941-972, Rio de Janeiro, Brazil and Instituto de Matemática, Universidade Fe ...;COPPE/Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21941-972, Rio de Janeiro, Brazil;COPPE/Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21941-972, Rio de Janeiro, Brazil and Instituto de Matemática, Universidade Fe ...
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 3
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Unit and single point interval graphs

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Abstract

Given an interval graph G, the interval count problem is that of computing the minimum number IC(G) of interval lengths needed to represent G. Although the problem of deciding whether IC(G)=1 is equivalent to that of recognizing unit-interval graphs, which is a well-known problem having several efficient recognition approaches, very little is known about deciding efficiently whether IC(G)=k for fixed k=2. We provide efficient computations of the interval count of generalizations of threshold graphs.