Results 21 to 30 of about 119,018,322 (196)
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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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 \(0\leq r\leq k-2\).
D. T. Busolini, Paul Erdös
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On a valence problem in extremal graph theory
Discrete Mathematics, 1973 Vorliegende Arbeit bezieht sich auf nicht-orientierte, Schlingen und mehrfache Kanten nicht enhaltende Graphen. Bezeichne \(L\) einen solchen vom vollständigen \(p\)-Graphen \(K_p\) verschiedenen \(p\)-chromatischen Graphen, welcher eine Kante \(e\) so enthält, daß \(L-e\) ein \((p-1)\)-chromatischer Graph ist. Als Hauptergebnis der vorliegenden Arbeit
Paul Erdös, Miklós Simonovits
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On the number of pentagons in triangle-free graphs [PDF]
, 2013 Using the formalism of flag algebras, we prove that every triangle-free graph G with n vertices contains at most (n/5)(5) cycles of length five. Moreover, the equality is attained only when n is divisible by five and G is the balanced blow-up of the ...
Hatami, Hamed +4 more
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Proofs by Transformation in Extremal Graph Theory [PDF]
, 2022 A graph is a mathematical model representing binary relationships between elements of a set. It is composed of two sets: the set of the elements called the vertices and a set of pairs of vertices called the edges.
Devillez, Gauvain
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Extremal Infinite Graph Theory
, 2010 We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree.
Maya Stein, Stein, Maya
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Advanced Functional Materials, EarlyView.Neuromorphic plasticity in OECTs is governed by the post‐stimulus evolution of coupled ionic and electronic states. Semiconductor chemistry and morphology, electrolyte composition and interfaces, and device architecture regulate ion injection, transport, confinement, and release, shifting responses from rapidly relaxing STP to metastable memory and ...
Inho Lee +9 more
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Rational exponents in extremal graph theory [PDF]
, 2016 Given a family of graphs H, the extremal number ex(n,H) is the largest m for which there exists a graph with n vertices and m edges containing no graph from the family H as a subgraph.
David Conlon +3 more
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Advanced Materials, EarlyView.This review highlights the role of self‐assembled monolayers (SAMs) in perovskite solar cells, covering molecular engineering, multifunctional interface regulation, machine learning (ML) accelerated discovery, advanced device architectures, and pathways toward scalable fabrication and commercialization for high‐efficiency and stable single‐junction and
Asmat Ullah, Ying Luo, Stefaan De Wolf
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Organic Materials of Tomorrow: Horizons of Artificial Intelligence
Advanced Materials, EarlyView.This review examines machine learning techniques accelerating the discovery of organic semiconductors by linking molecular structure to properties. Key methods include graph neural networks, generative models, and active learning. Applications to organic photovoltaics demonstrate practical impact.
Harold Mena +3 more
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