On the Classes of Interval Graphs of Limited Nesting and Count of Lengths

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332310" target="_blank" >RIV/00216208:11320/16:10332310 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45" target="_blank" >10.4230/LIPIcs.ISAAC.2016.45</a>

Result language
angličtina
Original language name
On the Classes of Interval Graphs of Limited Nesting and Count of Lengths
Original language description
In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called k-length interval graphs were considered in which the number of different lengths of intervals is limited by k. Even after decades of research, no insight into their structure is known and the complexity of recognition is open even for k = 2. We propose generalizations of proper interval graphs called k-nested interval graphs in which there are no chains of k + 1 intervals nested in each other. It is easy to see that k-nested interval graphs are a superclass of k-length interval graphs. We give a linear-time recognition algorithm for k-nested interval graphs. This algorithm adds a missing piece to Gajarský et al. [FOCS 2015] to show that testing FO properties on interval graphs is FPT with respect to the nesting k and the length of the formula, while the problem is W[2]-hard when parameterized just by the length of the formula. Further, we show that a generalization of recognition called partial representation extension is polynomial-time solvable for k-nested interval graphs, while it is NP-hard for k-length interval graphs, even when k = 2.
Czech name
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Czech description
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Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
27th International Symposium on Algorithms and Computation (ISAAC 2016)
ISBN
978-3-95977-026-2
ISSN
1868-8969
e-ISSN
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Number of pages
13
Pages from-to
1-13
Publisher name
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Sydney
Event date
Dec 12, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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