335 research outputs found
The history of degenerate (bipartite) extremal graph problems
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.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Rational exponents in extremal graph theory
Given a family of graphs , the extremal number is the largest for which there exists a graph with
vertices and edges containing no graph from the family as a
subgraph. We show that for every rational number between and , there
is a family of graphs such that . This solves a longstanding problem in the area of extremal
graph theory.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1411.085
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