TWIN-WIDTH AND PERMUTATIONS

被引：0
|
作者：
Bonnet, Edouard [1 ]
Nesetril, Jaroslav [2 ]
De Mendez, Patrice Ossona [2 ,3 ]
Siebertz, Sebastian [4 ]
Thomasse, Stephan [1 ]
机构：
[1] Univ Lyon, ENS Lyon, CNRS, Lyon, France
[2] Charles Univ IUUK, Comp Sci Inst, Prague, Czech Republic
[3] CNRS, UMR 8557, Ctr Anal & Math Sociales, EHESS, Paris, France
[4] Univ Bremen, Bremen, Germany
来源：
LOGICAL METHODS IN COMPUTER SCIENCE | 2024年 / 20卷 / 03期
基金：
欧洲研究理事会;
关键词：
Twin-width; first-order transductions; structural graph theory;
D O I：
10.46298/LMCS-20(3:4)2024
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomasse, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been further extended to binary structures, in several (basically equivalent) ways. We prove that a class of binary relational structures (that is: edge-colored partially directed graphs) has bounded twin-width if and only if it is a first-order transduction of a proper permutation class. As a by-product, we show that every class with bounded twin-width contains at most 2(O(n)) pairwise non-isomorphic n-vertex graphs.
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收藏
页码：1 / 25
页数：25
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