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Two Extremal Problems in Graph Theory
The Electronic Journal of Combinatorics, 1994 We consider the following two problems. (1) Let $t$ and $n$ be positive integers with $n\geq t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that contains neither $K_t$ nor $K_{t,t}$ as a subgraph. (2) Let $r$, $t$ and $n$ be positive integers with $n\geq rt$ and $t\geq 2$. Determine the maximum number of edges of a graph of
Brualdi, Richard A., Mellendorf, Stephen
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The history of degenerate (bipartite) extremal graph problems [PDF]
, 2013 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.
A. A. Razborov +198 more
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On an extremal problem in graph theory [PDF]
Colloquium Mathematicum, 1964 Let \(l\) and \(p\) be integers such that \(l>p\). It is shown that there exists a constant \(\gamma_{p,l}\) such that if \(n>n_0(p,l)\) then every graph with \(n\) vertices and \([\gamma_{p,l}n^{2-1/p}]\) edges contains a subgraph \(H\) with the following property: the vertices of \(H\) may be labbeled \(x_1,...,x_l\) and \(y_1,...,y_l\) so that every
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Finitely forcible graphons with an almost arbitrary structure
Discrete Analysis, 2020 Finitely forcible graphons with an almost arbitrary structure, Discrete Analysis 2020:9, 36 pp. A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if $G$ is a graph with $n$ vertices and density $p$, and if the number ...
Daniel Kral +3 more
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An advance in infinite graph models for the analysis of transportation networks
International Journal of Applied Mathematics and Computer Science, 2016 This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph.
Cera Martín, Fedriani Eugenio M.
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On a problem in extremal graph theory
Journal of Combinatorial Theory, Series B, 1977 From the authors introduction. Let \(G(n,m)\) denote a graph \((V,E)\) with \(n\) vertices and \(m\) edges and \(K_1\) a complete graph with \(i\) vertices. \textit{P.Turán} proved that every \(G(n,T(n,k))\) contains a \(K_k\), where \[ T(n,k) = \frac{k-2}{2(k-1)}(n^2-r^2)+\binom r2+1, \] \(r\equiv n(\mod k-1)\) and \(0\leq r\leq k-2\).
Busolini, D.T, Erdös, P
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Maximum Cycle Packing in Eulerian Graphs Using Local Traces
Discussiones Mathematicae Graph Theory, 2015 For a graph G = (V,E) and a vertex v ∈ V , let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walk W(v), with start vertex v can be extended to an Eulerian tour in T(v).
Recht Peter, Sprengel Eva-Maria
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Extremal problems for the p-spectral radius of graphs [PDF]
, 2014 The $p$-spectral radius of a graph $G\ $of order $n$ is defined for any real number $p\geq1$ as \[ \lambda^{\left( p\right) }\left( G\right) =\max\left\{ 2\sum_{\{i,j\}\in E\left( G\right) \ }x_{i}x_{j}:x_{1},\ldots,x_{n}\in\mathbb{R}\text{ and }\left ...
Kang, Liying, Nikiforov, Vladimir
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Largest minimally inversion-complete and pair-complete sets of permutations [PDF]
, 2017 We solve two related extremal problems in the theory of permutations. A set Q of permutations of the integers 1 to n is inversion-complete (resp., pair-complete) if for every inversion (j; i), where 1 j), where i 6= j), there exists a permutation in Q ...
Balandraud, Eric +2 more
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Extremal numbers for odd cycles [PDF]
, 2013 We describe the C_{2k+1}-free graphs on n vertices with maximum number of edges. The extremal graphs are unique except for n = 3k-1, 3k, 4k-2, or 4k-1. The value of ex(n,C_{2k+1}) can be read out from the works of Bondy, Woodall, and Bollobas, but here ...
Füredi, Zoltan, Gunderson, David S.
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