Minimal Obstructions for Partial Representations of Interval Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43925017" target="_blank" >RIV/49777513:23520/14:43925017 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007/978-3-319-13075-0_32" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-319-13075-0_32</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-13075-0_32" target="_blank" >10.1007/978-3-319-13075-0_32</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Minimal Obstructions for Partial Representations of Interval Graphs

Popis výsledku v původním jazyce

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. In this paper, we characterize the minimal obstructions which make a partial representation non-extendible. This generalizes Lekkerkerker and Boland's characterization of minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible ifand only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to the first polynomial-time certifying algorithm for partial representation extension of intersection graphs.

Název v anglickém jazyce

Minimal Obstructions for Partial Representations of Interval Graphs

Popis výsledku anglicky

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. In this paper, we characterize the minimal obstructions which make a partial representation non-extendible. This generalizes Lekkerkerker and Boland's characterization of minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible ifand only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to the first polynomial-time certifying algorithm for partial representation extension of intersection graphs.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: Nová excelence lidských zdrojů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Lecture Notes in Computer Science

ISSN

0302-9743

e-ISSN

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Svazek periodika

8889

Číslo periodika v rámci svazku

2014

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

401-413

Kód UT WoS článku

000354865900032

EID výsledku v databázi Scopus

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