Extending Partial Representations of Circular-Arc Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455448" target="_blank" >RIV/00216208:11320/22:10455448 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-15914-5_17" target="_blank" >https://doi.org/10.1007/978-3-031-15914-5_17</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-15914-5_17" target="_blank" >10.1007/978-3-031-15914-5_17</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extending Partial Representations of Circular-Arc Graphs

Popis výsledku v původním jazyce

The partial representation extension problem generalizes the recognition problem for classes of graphs defined in terms of geometric representations. We consider this problem for circular-arc graphs, where several arcs are predrawn and we ask whether this partial representation can be completed. We show that this problem is NP-complete for circular-arc graphs, answering a question of Klavik et al. (2014). We complement this hardness with tractability results of the representation extension problem for various subclasses of circular-arc graphs. We give linear-time algorithms for extending normal proper Helly and proper Helly representations. For normal Helly circular-arc representations we give an O(n(3))-time algorithm where n is the number of vertices. Surprisingly, for Helly representations, the complexity hinges on the seemingly irrelevant detail of whether the predrawn arcs have distinct or non-distinct endpoints: In the former case the algorithm for normal Helly circular-arc representations can be extended, whereas the latter case turns out to be NP-complete. We also prove that the partial representation extension problem for unit circular-arc graphs is N P-complete.

Název v anglickém jazyce

Extending Partial Representations of Circular-Arc Graphs

Popis výsledku anglicky

The partial representation extension problem generalizes the recognition problem for classes of graphs defined in terms of geometric representations. We consider this problem for circular-arc graphs, where several arcs are predrawn and we ask whether this partial representation can be completed. We show that this problem is NP-complete for circular-arc graphs, answering a question of Klavik et al. (2014). We complement this hardness with tractability results of the representation extension problem for various subclasses of circular-arc graphs. We give linear-time algorithms for extending normal proper Helly and proper Helly representations. For normal Helly circular-arc representations we give an O(n(3))-time algorithm where n is the number of vertices. Surprisingly, for Helly representations, the complexity hinges on the seemingly irrelevant detail of whether the predrawn arcs have distinct or non-distinct endpoints: In the former case the algorithm for normal Helly circular-arc representations can be extended, whereas the latter case turns out to be NP-complete. We also prove that the partial representation extension problem for unit circular-arc graphs is N P-complete.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GC19-17314J" target="_blank" >GC19-17314J: Geometrické reprezentace grafů</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE (WG 2022)

ISBN

978-3-031-15914-5

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

14

Strana od-do

230-243

Název nakladatele

SPRINGER INTERNATIONAL PUBLISHING AG

Místo vydání

CHAM

Místo konání akce

Tubingen

Datum konání akce

22. 6. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000866013700017