• Corpus ID: 14017325

# AN EXTREMAL PROBLEM IN GRAPH THEORY

```@inproceedings{Preston2001ANEP,
title={AN EXTREMAL PROBLEM IN GRAPH THEORY},
author={G. B. Preston},
year={2001}
}```
G(?z; I) will denote a graph of n vertices and 1 edges. Let fO(lz, K) be the smallest integer such that there is a G (n; f,, (n, k)) in which for every set of K vertices there is a vertex joined to each of these. Thus for example fO(3, 2) = 3 since in a triangle each pair of vertices is joined to a third. It can readily be checked that f,(4, 2) = 5 (the extremal graph consists of a complete 4-gon with one edge removed). In general we will prove: Let n > k, and
419 Citations
The Erdős-Sós Conjecture for Geometric Graphs
• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2013
This paper completely solve the problem and prove that at least three edges must be removed from some complete geometric graph G on n points and G is a geometric graph on a set of points in convex position.
A new generalization of Mantel's theorem to k-graphs
• Mathematics
J. Comb. Theory, Ser. B
• 2007
Results in Extremal Graph and Hypergraph Theory
In graph theory, as in many fields of mathematics, one is often interested in finding the maxima or minima of certain functions and identifying the points of optimality. We consider a variety of
On a conjecture of spectral extremal problems
• Mathematics
• 2022
For a simple graph F , let Ex(n, F ) and Exsp(n, F ) denote the set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an n-vertex graph without any
An efficient algorithm for the density Turán problem of some unicyclic graphs
• Mathematics
2014 Federated Conference on Computer Science and Information Systems
• 2014
An efficient algorithm is shown to decide whether a given set of edge densities ensures the existence of H in the blow-up graph G[H]; this problem for unicyclic graphs H with the cycle C3 is studied.
Sets of elements that pairwise generate a linear group
• Mathematics
J. Comb. Theory, Ser. A
• 2008
Full subgraphs
• Mathematics
J. Graph Theory
• 2018
Following Erdős, Luczak and Spencer, an m-vertex subgraph H of G is called full if H has minimum degree at least p(m−1) and f(G) denote the order of a largest full subgraph of G.
The Turán number of the graph 3P5
• Mathematics
• 2020
The Turán number ex(n,H) of a graph H, is the maximum number of edges in a graph of order n which does not contain H as a subgraph. Let Ex(n,H) denote all H-free graphs on n vertices with ex(n,H)
A ug 2 02 1 The spectral extremal graphs containing no intersecting cliques ∗
• Mathematics
• 2021
In this paper we consider spectral extremal problem for graphs without intersecting cliques. Let Ex(n, F ) be the set of graphs with the maximum number of edges in a graph on n vertices not