Asymptotic dimension of intersection graphs

被引：0
|
作者：
Dvorak, Zdenek [1 ]
Norin, Sergey [2 ]
机构：
[1] Charles Univ Prague, Prague, Czech Republic
[2] McGill Univ, Montreal, PQ, Canada
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2025年 / 123卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1016/j.ejc.2022.103631
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that intersection graphs of compact convex sets in R(n )of bounded aspect ratio have asymptotic dimension at most 2n+ 1. More generally, we show this is the case for intersection graphs of systems of subsets of any metric space of Assouad- Nagata dimension n that satisfy the following condition: For each r, s > 0 and every point p, the number of pairwise-disjoint elements of diameter at least s in the system that are at distance at most r from p is bounded by a function of r/s. (c) 2022 Elsevier Ltd. All rights reserved.
引用
收藏
页数：10
相关论文
共 50 条
  • [41] PROPERTY A AND ASYMPTOTIC DIMENSION
    Cencelj, Matija
    Dydak, Jerzy
    Vavpetic, Ales
    GLASNIK MATEMATICKI, 2012, 47 (02) : 441 - 444
  • [42] On the Intersection of Tolerance and Cocomparability Graphs
    Mertzios, George B.
    Zaks, Shmuel
    ALGORITHMS AND COMPUTATION, PT I, 2010, 6506 : 230 - 240
  • [43] RANDOM INTERSECTION GRAPHS WITH COMMUNITIES
    van der Hofstad, Remco
    Komjathy, Julia
    Vadon, Viktoria
    ADVANCES IN APPLIED PROBABILITY, 2021, 53 (04) : 1061 - 1089
  • [44] RECTANGLE INTERSECTION AND OVERLAP GRAPHS
    RIM, CS
    NAKAJIMA, K
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1995, 42 (09) : 549 - 553
  • [45] INTERSECTION-PROPERTIES OF GRAPHS
    MCKEE, TA
    DISCRETE MATHEMATICS, 1991, 89 (03) : 253 - 260
  • [46] Coset Intersection Graphs for Groups
    Button, Jack
    Chiodo, Maurice
    Laris, Mariano Zeron-Medina
    AMERICAN MATHEMATICAL MONTHLY, 2014, 121 (10): : 922 - 926
  • [47] On the structure of certain intersection graphs
    Cameron, Kathie
    Hoang, Chinh T.
    INFORMATION PROCESSING LETTERS, 2006, 99 (02) : 59 - 63
  • [48] Approximation Algorithms for Intersection Graphs
    Kammer, Frank
    Tholey, Torsten
    ALGORITHMICA, 2014, 68 (02) : 312 - 336
  • [49] Approximation Algorithms for Intersection Graphs
    Kammer, Frank
    Tholey, Torsten
    Voepel, Heiko
    APPROXIMATION, RANDOMIZATION, AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, 2010, 6302 : 260 - 273
  • [50] Intersection graphs of rectangles and segments
    Ahlswede, R.
    Karapetyan, I.
    GENERAL THEORY OF INFORMATION TRANSFER AND COMBINATORICS, 2006, 4123 : 1064 - +
12345