Characterizations of cographs as intersection graphs of paths on a grid

Elad Cohen; Martin Charles Golumbic; Bernard Ries

doi:10.1016/j.dam.2014.06.020

Characterizations of cographs as intersection graphs of paths on a grid

Elad Cohen, Martin Charles Golumbic, Bernard Ries

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A cograph is a graph which does not contain any induced path on four vertices. In this paper, we characterize those cographs that are intersection graphs of paths on a grid in the following two cases: (i) the paths on the grid all have at most one bend and the intersections concern edges (→ B₁-EPG); (ii) the paths on the grid are not bended and the intersections concern vertices (→ B₀-VPG). In both cases, we give a characterization by a family of forbidden induced subgraphs. We further present linear-time algorithms to recognize B₁-EPG cographs and B₀-VPG cographs using their cotree.

Original language	English
Pages (from-to)	46-57
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	178
DOIs	https://doi.org/10.1016/j.dam.2014.06.020
State	Published - 11 Dec 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.

Keywords

Cograph
Cotree
Grid
Induced subgraph
Intersection graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2014.06.020

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title = "Characterizations of cographs as intersection graphs of paths on a grid",

abstract = "A cograph is a graph which does not contain any induced path on four vertices. In this paper, we characterize those cographs that are intersection graphs of paths on a grid in the following two cases: (i) the paths on the grid all have at most one bend and the intersections concern edges (→ B1-EPG); (ii) the paths on the grid are not bended and the intersections concern vertices (→ B0-VPG). In both cases, we give a characterization by a family of forbidden induced subgraphs. We further present linear-time algorithms to recognize B1-EPG cographs and B0-VPG cographs using their cotree.",

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AU - Golumbic, Martin Charles

AU - Ries, Bernard

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N2 - A cograph is a graph which does not contain any induced path on four vertices. In this paper, we characterize those cographs that are intersection graphs of paths on a grid in the following two cases: (i) the paths on the grid all have at most one bend and the intersections concern edges (→ B1-EPG); (ii) the paths on the grid are not bended and the intersections concern vertices (→ B0-VPG). In both cases, we give a characterization by a family of forbidden induced subgraphs. We further present linear-time algorithms to recognize B1-EPG cographs and B0-VPG cographs using their cotree.

AB - A cograph is a graph which does not contain any induced path on four vertices. In this paper, we characterize those cographs that are intersection graphs of paths on a grid in the following two cases: (i) the paths on the grid all have at most one bend and the intersections concern edges (→ B1-EPG); (ii) the paths on the grid are not bended and the intersections concern vertices (→ B0-VPG). In both cases, we give a characterization by a family of forbidden induced subgraphs. We further present linear-time algorithms to recognize B1-EPG cographs and B0-VPG cographs using their cotree.

KW - Cograph

KW - Cotree

KW - Grid

KW - Induced subgraph

KW - Intersection graph

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DO - 10.1016/j.dam.2014.06.020

M3 - Article

AN - SCOPUS:84907711802

SN - 0166-218X

VL - 178

SP - 46

EP - 57

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Characterizations of cographs as intersection graphs of paths on a grid

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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