Extending Partial Representations of Circular-Arc Graphs

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Extending Partial Representations of Circular-Arc Graphs

Original language description

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.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GC19-17314J" target="_blank" >GC19-17314J: Geometric Representations of Graphs</a><br>

Continuities

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

Publication year

2022

Confidentiality

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

Article name in the collection

GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE (WG 2022)

ISBN

978-3-031-15914-5

ISSN

0302-9743

e-ISSN

1611-3349

Number of pages

14

Pages from-to

230-243

Publisher name

SPRINGER INTERNATIONAL PUBLISHING AG

Place of publication

CHAM

Event location

Tubingen

Event date

Jun 22, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000866013700017