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
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