Results 1 to 10 of about 25,547 (250)
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory. [PDF]
Entropy (Basel), 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures.
Sason I.
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Turan problems in extremal graph theory and flexibility
, 2021 In this work we will study two distinct areas of graph theory: generalized Turan problems and graph flexibility. In the first chapter, we will provide some basic definitions and motivation. Chapters 2 and 3 contain two submitted papers showing that two graphs, the cycle on five vertices and the path on four vertices, are maximized by the Turan graph ...
Kyle Murphy
semanticscholar +6 more sources
Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory
, 2015 In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
Bhargav Narayanan
semanticscholar +4 more sources
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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Some Problems in Algebraic and Extremal Graph Theory.
, 1995 In this dissertation, we consider a wide range of problems in algebraic and extremal graph theory. In extremal graph theory, we will prove that the Tree Packing Conjecture is true for all sequences of trees th a t are ‘almost stars’; and we prove tha t ...
Edward Dobson
semanticscholar +4 more sources
Some problems in extremal graph theory avoiding the use of the regularity lemma
, 2009 In this thesis we present two results in Extremal Graph Theory. The first result is a new proof of a conjecture of Bollobas on embedding trees of bounded degree. The second result is a new proof of the Posa conjecture.Let G=(W,E) be a graph on n vertices having minimum degree at least n/2 + c log(n), where c is a constant.
Ian Levitt
semanticscholar +3 more sources
Extremal Problems in Discrete Geometry and Spectral Graph Theory
, 2019 Igor Balla
semanticscholar +4 more sources
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.
H. L. Abbott, Meir Katchalski, A. C. Liu
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On some interconnections between combinatorial optimization and extremal graph theory [PDF]
Yugoslav Journal of Operations Research, 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.
Cvetković Dragoš M. +2 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
Péter L. Erdős
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