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@inproceedings{2227560,
author = {Balabán, Jakub and Hliněný, Petr and Jedelský, Jan},
address = {Cham},
booktitle = {WG 2022: Graph-Theoretic Concepts in Computer Science},
doi = {http://dx.doi.org/10.1007/978-3-031-15914-5_4},
edition = {LNCS 13453},
editor = {Michael A. Bekos and Michael Kaufmann},
keywords = {twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Cham},
isbn = {978-3-031-15913-8},
pages = {43-55},
publisher = {Springer Nature},
title = {Twin-Width and Transductions of Proper k-Mixed-Thin Graphs},
url = {https://link.springer.com/chapter/10.1007/978-3-031-15914-5_4},
year = {2022}
}
TY - JOUR
ID - 2227560
AU - Balabán, Jakub - Hliněný, Petr - Jedelský, Jan
PY - 2022
TI - Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
PB - Springer Nature
CY - Cham
SN - 9783031159138
KW - twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence
UR - https://link.springer.com/chapter/10.1007/978-3-031-15914-5_4
N2 - The new graph parameter twin-width, recently introduced by Bonnet et al., 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, such classes (of small 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 certain subclass of k-mixed-thin graphs is transduction-equivalent to posets of width 𝑘′ such that there is a quadratic relation between k and 𝑘′.
ER -
BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ. Twin-Width and Transductions of Proper k-Mixed-Thin Graphs. In Michael A. Bekos and Michael Kaufmann. \textit{WG 2022: Graph-Theoretic Concepts in Computer Science}. LNCS 13453. Cham: Springer Nature, 2022, p.~43-55. ISBN~978-3-031-15913-8. Available from: https://dx.doi.org/10.1007/978-3-031-15914-5\_{}4.
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