The History of Degenerate (Bipartite) Extremal Graph Problems

By Z. Furedi, Miklós Simonovits. 2013

438 citations recorded by the source corpus.

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.

View Paper: https://www.semanticscholar.org/paper/448dc7527c4031086bcdf3d117e73bc163b64c5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. David Conlon
2. Yongtao Li
3. Weijun Liu
4. Lihua Feng
5. Dheer Noal Desai
6. Michael Tait
7. Liying Kang
8. Zhenyu Ni

Citations in the corpus

• Spectral extremal graphs for intersecting cliques (2021, methodology): “Since χ(Fk) = 3, the Erdős–Stone–Simonovits theorem in (1) implies that ex(n, Fk) = n 2/4 + o(n2).”
• Rational exponents in extremal graph theory (2015, background): “This solves a longstanding problem in the area of extremal graph theory.”
• A survey on spectral conditions for some extremal graph problems (2021, background): “The most celebrated extension always attributes to a result of Erdős, Stone and Simonovits [60, 66], which states that ex(n, F ) = ( 1− 1 χ(F )− 1 + o(1) ) n2 2 , where χ(F ) is the vertex-chromatic number of F .”