Twin-Width and Transductions of Proper k-Mixed-Thin Graphs

J 2024

Twin-Width and Transductions of Proper k-Mixed-Thin Graphs

BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ

Basic information

Original name

Twin-Width and Transductions of Proper k-Mixed-Thin Graphs

Authors

BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ

Edition

DISCRETE MATHEMATICS, NETHERLANDS, ELSEVIER, 2024, 0012-365X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.800 in 2022

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.disc.2024.113876

Keywords in English

twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence

Abstract

V originále

The new graph parameter twin-width, introduced by Bonnet, Kim, Thomassé and Watrigant in 2020, allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the algorithmic point of view. In particular, classes of efficiently bounded twin-width include proper interval graphs, and (as digraphs) posets of width k. Inspired by an existing generalization of interval graphs into so-called k-thin graphs, we define a new class of proper k-mixed-thin graphs which largely generalizes proper interval graphs. We prove that proper k-mixed-thin graphs have twin-width linear in k, and that a slight subclass of k-mixed-thin graphs is transduction-equivalent to posets of width such that there is a quadratic-polynomial relation between k and . In addition to that, we also give an abstract overview of the so-called red potential method which we use to prove our twin-width bounds.

Links

MUNI/A/1592/2023, interní kód MU

Name: Modelování, analýza a verifikace (2024)

Investor: Masaryk University, Modeling, analysis, and verification (2024)

MUNI/A/1608/2023, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 24

Investor: Masaryk University

Citovat

BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ. Twin-Width and Transductions of Proper k-Mixed-Thin Graphs. DISCRETE MATHEMATICS. NETHERLANDS: ELSEVIER, 2024, vol. 347, No 8, 20 pp. ISSN 0012-365X. Available from: https://dx.doi.org/10.1016/j.disc.2024.113876.

@article{2374737,
   author = {Balabán, Jakub and Hliněný, Petr and Jedelský, Jan},
   article_location = {NETHERLANDS},
   article_number = {8},
   doi = {http://dx.doi.org/10.1016/j.disc.2024.113876},
   keywords = {twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence},
   language = {eng},
   issn = {0012-365X},
   journal = {DISCRETE MATHEMATICS},
   title = {Twin-Width and Transductions of Proper k-Mixed-Thin Graphs},
   url = {https://arxiv.org/abs/2202.12536},
   volume = {347},
   year = {2024}
}

TY  - JOUR
ID  - 2374737
AU  - Balabán, Jakub - Hliněný, Petr - Jedelský, Jan
PY  - 2024
TI  - Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
JF  - DISCRETE MATHEMATICS
VL  - 347
IS  - 8
PB  - ELSEVIER
SN  - 0012365X
KW  - twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence
UR  - https://arxiv.org/abs/2202.12536
N2  - The new graph parameter twin-width, introduced by Bonnet, Kim, Thomassé and Watrigant in 2020, allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the algorithmic point of view. In particular, classes of efficiently bounded twin-width include proper interval graphs, and (as digraphs) posets of width k. Inspired by an existing generalization of interval graphs into so-called k-thin graphs, we define a new class of proper k-mixed-thin graphs which largely generalizes proper interval graphs. We prove that proper k-mixed-thin graphs have twin-width linear in k, and that a slight subclass of k-mixed-thin graphs is transduction-equivalent to posets of width such that there is a quadratic-polynomial relation between k and . In addition to that, we also give an abstract overview of the so-called red potential method which we use to prove our twin-width bounds.
ER  -

BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ. Twin-Width and Transductions of Proper k-Mixed-Thin Graphs. \textit{DISCRETE MATHEMATICS}. NETHERLANDS: ELSEVIER, 2024, vol.~347, No~8, 20 pp. ISSN~0012-365X. Available from: https://dx.doi.org/10.1016/j.disc.2024.113876.

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