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@article{2374737, author = {Balabán, Jakub and Hliněný, Petr and Jedelský, Jan}, article_location = {NETHERLANDS}, 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}, 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 SP - to appear EP - to appear 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 a Jan JEDELSKÝ. Twin-Width and Transductions of Proper k-Mixed-Thin Graphs. \textit{DISCRETE MATHEMATICS}. NETHERLANDS: ELSEVIER, 2024, s.~to appear, 20 s. ISSN~0012-365X. Dostupné z: https://dx.doi.org/10.1016/j.disc.2024.113876.
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