First Order Limits of Sparse Graphs: Plane Trees and Path-Width

被引：3

作者：

Gajarsky, Jakub ^{[1
]}

Hlineny, Petr ^{[1
]}

Kaiser, Tomas ^{[2
,3
]}

Kral, Daniel ^{[4
,5
]}

Kupec, Martin ^{[6
]}

Obdrzalek, Jan ^{[1
]}

Ordyniak, Sebastian ^{[1
]}

Tuma, Vojtech ^{[7
]}

机构：

[1] Masaryk Univ, Fac Informat, Bot 68a, Brno 60200, Czech Republic

[2] Univ West Bohemia, Inst Theoret Comp Sci CE ITI, Dept Math, Univ 8, Plzen 30614, Czech Republic

[3] Univ West Bohemia, European Ctr Excellence, NTIS, Univ 8, Plzen 30614, Czech Republic

[4] Univ Warwick, DIMAP, Math Inst, Coventry CV4 7AL, W Midlands, England

[5] Univ Warwick, Dept Comp Sci, Coventry CV4 7AL, W Midlands, England

[6] Charles Univ Prague, Fac Math & Phys, Comp Sci Inst, Malostranske Namesti 25, Prague 11800, Czech Republic

[7] Charles Univ Prague, Fac Math & Phys, Dept Appl Math, Malostranske Namesti 25, Prague 11800, Czech Republic

来源：

RANDOM STRUCTURES & ALGORITHMS | 2017年 / 50卷 / 04期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

graph limits; graphs with bounded path-width; first order limits; first order logic; CONVERGENT SEQUENCES;

D O I：

10.1002/rsa.20676

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Nesetril and Ossona de Mendez introduced the notion of first order convergence as an attempt to unify the notions of convergence for sparse and dense graphs. It is known that there exist first order convergent sequences of graphs with no limit modeling (an analytic representation of the limit). On the positive side, every first order convergent sequence of trees or graphs with no long path (graphs with bounded tree-depth) has a limit modeling. We strengthen these results by showing that every first order convergent sequence of plane trees (trees with embeddings in the plane) and every first order convergent sequence of graphs with bounded path-width has a limit modeling. (C) 2016 Wiley Periodicals, Inc.

引用

页码：612 / 635

页数：24

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