Minimal Obstructions for Partial Representations of Interval Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10288454" target="_blank" >RIV/00216208:11320/14:10288454 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007%2F978-3-319-13075-0_32" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-319-13075-0_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

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název statě ve sborníku

Algorithms and Computation

ISBN

978-3-319-13074-3

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

13

Strana od-do

401-413

Název nakladatele

Springer International Publishing

Místo vydání

Switzerland

Místo konání akce

Jeonju, South Korea

Datum konání akce

15. 12. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—