Rational exponents in extremal graph theory

被引：29
|
作者：
Bukh, Boris [1 ]
Conlon, David [2 ]
机构：
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
[2] Math Inst, Oxford OX2 6GG, England
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2018年 / 20卷 / 07期
基金：
欧洲研究理事会;
关键词：
Extremal graph theory; bipartite graphs; algebraic constructions; NORM-GRAPHS;
D O I：
10.4171/JEMS/798
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a family H of graphs, the extremal number ex(n, H) is the largest m for which there exists a graph with n vertices and m edges containing no graph from the family H as a subgraph. We show that for every rational number r between 1 and 2, there is a family H-r of graphs such that ex(n, H-r) = Theta(n(r)). This solves a longstanding problem in extremal graph theory.
引用
收藏
页码：1747 / 1757
页数：11
相关论文
共 50 条
  • [31] Theory of extremal dynamics with quenched disorder: Self-organization, avalanche dynamics and critical exponents
    Cafiero, R
    Pietronero, L
    Gabrielli, A
    Marsili, M
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 1998, 12 (12-13): : 1263 - 1275
  • [32] Theory of extremal dynamics with quenched disorder: self-organization, avalanches dynamics and critical exponents
    Gabrielli, A
    Cafiero, R
    Pietronero, L
    Marsili, M
    PHYSICS OF COMPLEX SYSTEMS, 1997, 134 : 746 - 746
  • [33] Critical exponents for the Pucci's extremal operators
    Felmer, PL
    Quaas, A
    COMPTES RENDUS MATHEMATIQUE, 2002, 335 (11) : 909 - 914
  • [34] Extremal exponents of random products of conservative diffeomorphisms
    Pablo G. Barrientos
    Dominique Malicet
    Mathematische Zeitschrift, 2020, 296 : 1185 - 1207
  • [35] Extremal Lyapunov exponents: an invariance principle and applications
    Artur Avila
    Marcelo Viana
    Inventiones mathematicae, 2010, 181 : 115 - 178
  • [36] Critical exponents for uniformly elliptic extremal operators
    Felmer, Patricio L.
    Quaas, Alexander
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (02) : 593 - 629
  • [37] On semigroup algebras with rational exponents
    Gotti, Felix
    COMMUNICATIONS IN ALGEBRA, 2022, 50 (01) : 3 - 18
  • [38] On critical exponents for the Pucci's extremal operators
    Felmer, PL
    Quaas, A
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2003, 20 (05): : 843 - 865
  • [39] Extremal exponents of random products of conservative diffeomorphisms
    Barrientos, Pablo G.
    Malicet, Dominique
    MATHEMATISCHE ZEITSCHRIFT, 2020, 296 (3-4) : 1185 - 1207
  • [40] Extremal Lyapunov exponents: an invariance principle and applications
    Avila, Artur
    Viana, Marcelo
    INVENTIONES MATHEMATICAE, 2010, 181 (01) : 115 - 178
12345