Results 21 to 30 of about 34,690 (269)
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
Richard A. Brualdi, Stephen Mellendorf
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Hypergraphs with infinitely many extremal constructions
Discrete Analysis, 2023 Hypergraphs with infinitely many extremal constructions, Discrete Analysis 2023:18, 34 pp. A fundamental result in extremal graph theory, Turán's theorem, states that the maximal number of edges of a graph with $n$ vertices that does not contain a ...
Jianfeng Hou +4 more
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An extremal problem in graph theory II [PDF]
Journal of the Australian Mathematical Society, 1980 AbstractWe contine our study of the following combinatorial problem: What is the largest integer N = N (t, m, p) for which there exists a set of N people satisfying the following conditions: (a) each person speaks t languages, (b) among any m people there are two who speak a common language and (c) at most p speak a common language.
Abbott, H. L. +2 more
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Complexity, 2021 Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use.
Muhammad Asif +5 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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Asymptotic Structure for the Clique Density Theorem
Discrete Analysis, 2020 Asymptotic structure for the clique density theorem, Discrete Analysis 2020:19, 26 pp. Turán's theorem, which is regarded as the "first" result in extremal graph theory, is the statement that the $K_r$-free graph on $n$ vertices with the largest number ...
Jaehoon Kim +3 more
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Polytopes from Subgraph Statistics [PDF]
, 2011 Polytopes from subgraph statistics are important in applications and conjectures and theorems in extremal graph theory can be stated as properties of them.
Engström, Alexander, Norén, Patrik
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Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices [PDF]
Yugoslav Journal of Operations Research, 2019 The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G.
Devillez Gauvain +3 more
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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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An extremal problem in graph theory [PDF]
Journal of the Australian Mathematical Society, 1970 G(n;l) will denote a graph of n vertices and l edges. Let f0(n, k) be the smallest integer such that there is a G (n;f0(n, k)) in which for every set of k vertices there is a vertex joined to each of these. Thus for example fo = 3 since in a triangle each pair of vertices is joined to a third.
Erdős, Pál, Moser, L.
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