TY - JOUR

T1 - Max point-tolerance graphs

AU - Catanzaro, Daniele

AU - Chaplick, Steven

AU - Felsner, Stefan

AU - Halldórsson, Bjarni V.

AU - Halldórsson, Magnús M.

AU - Hixon, Thomas

AU - Stacho, Juraj

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2017

Y1 - 2017

N2 - A graph G is a max point-tolerance (MPT) graph if each vertex v of G can be mapped to a pointed-interval (I-v, P-v) where I-v is an interval of R and p(v) is an element of I-v such that uv is an edge of G iff I-u boolean AND I-v superset of {p(u) p(v)}. MPT graphs model relationships among DNA fragments in genomewide association studies as well as basic transmission problems in telecommunications. We formally introduce this graph class, characterize it, study combinatorial optimization problems on it, and relate it to several well known graph classes. We characterize MPT graphs as a special case of several 2D geometric intersection graphs; namely, triangle, rectangle, L-shape, and line segment intersection graphs. We further characterize MPT as having certain linear orders.on their vertex set. Our last characterization is that MPT graphs are precisely obtained by intersecting special pairs of interval graphs. We also show that, on MPT graphs, the maximum weight independent set problem can be solved in polynomial time, the coloring problem is NP-complete, and the clique cover problem has a 2-approximation. Finally, we demonstrate several connections to known graph classes; e.g., MPT graphs strictly contain interval graphs and outerplanar graphs, but are incomparable to permutation, chordal, and planar graphs. (C) 2015 Elsevier B.V. All rights reserved.

AB - A graph G is a max point-tolerance (MPT) graph if each vertex v of G can be mapped to a pointed-interval (I-v, P-v) where I-v is an interval of R and p(v) is an element of I-v such that uv is an edge of G iff I-u boolean AND I-v superset of {p(u) p(v)}. MPT graphs model relationships among DNA fragments in genomewide association studies as well as basic transmission problems in telecommunications. We formally introduce this graph class, characterize it, study combinatorial optimization problems on it, and relate it to several well known graph classes. We characterize MPT graphs as a special case of several 2D geometric intersection graphs; namely, triangle, rectangle, L-shape, and line segment intersection graphs. We further characterize MPT as having certain linear orders.on their vertex set. Our last characterization is that MPT graphs are precisely obtained by intersecting special pairs of interval graphs. We also show that, on MPT graphs, the maximum weight independent set problem can be solved in polynomial time, the coloring problem is NP-complete, and the clique cover problem has a 2-approximation. Finally, we demonstrate several connections to known graph classes; e.g., MPT graphs strictly contain interval graphs and outerplanar graphs, but are incomparable to permutation, chordal, and planar graphs. (C) 2015 Elsevier B.V. All rights reserved.

U2 - 10.1016/J.DAM.2015.08.019

DO - 10.1016/J.DAM.2015.08.019

M3 - Article

SN - 0166-218X

VL - 216

SP - 84

EP - 97

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -