Paper Info
Title
The minimum number of triangles in graphs of given order and size.
Abstract
Abstract In the 1940s and 50s, Erdős and Rademacher raised the quantitative question of determining the number of triangles one can guarantee in a graph of given order and size. This problem has garnered much attention and, in a major breakthrough, was solved asymptotically by Razborov in 2008, whose results were extended by Nikiforov and Reiher. In this paper, we provide an exact solution for all large graphs whose edge density is bounded away from one. This proves almost every case of a conjecture of Lovasz and Simonovits from 1975.
Year
DOI
Venue
2017
10.1016/j.endm.2017.07.039
Electronic Notes in Discrete Mathematics
Field
DocType
Volume
Exact solutions in general relativity,Discrete mathematics,Graph,Combinatorics,Edge density,Conjecture,Mathematics,Erdős–Gyárfás conjecture,Bounded function
Journal
61
Citations 
PageRank 
References 
0
0.34
2
Authors
3
Name
Order
Citations
PageRank
Hong Liu1398.54
Oleg Pikhurko231847.03
Katherine Staden363.31