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Information Inequalities via Submodularity and a Problem in Extremal Graph Theory

Entropy, 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.
Igal Sason
exaly   +6 more sources

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Two problems in extremal graph theory

Graphs and Combinatorics, 1986
P Erdos
exaly   +2 more sources

An extremal problem in graph theory

Israel Journal of Mathematics, 1968
It is proved that the maximum number of cut-vertices in a connected graph withn vertices andm edges is $$max\left\{ {q:m \leqq (_2^{n - q} ) + q} \right\}$$ All the extremal graphs are determined and the corresponding problem for cut-edges is also solved.
A Ramachandra Rao
exaly   +3 more sources

On an extremal problem concerning the theory of graphs

Archiv Der Mathematik, 1981
Chong-Yun Chao
exaly   +2 more sources

On some extremal problems in graph theory

Israel Journal of Mathematics, 1965
Der Verf. beweist, daß für eine genügend große Konstante \(c\) jeder Graph \(G\) mit \(n\) Punkten und \(cn^{3/2}\) Kanten ein Sechseck \(x_1,x_2,x_3,x_4,x_5,x_6\) enthält und dazu noch einen siebenten Punkt \(y\), der mit \(x_1,x_3\) und \(x_5\) verbunden ist.
P Erdos
exaly   +3 more sources

On an extremal inverse problem in graph theory

Journal of Applied and Industrial Mathematics, 2015
Summary: We consider the problem of constructing a graph having some given number of independent sets. The bounds are obtained for the number of vertices in bipartite graphs with the prescribed number of independent sets and for the number of inclusion maximal independent sets.
Daĭnyak, A. B., Kurnosov, A. D.
openaire   +2 more sources

Extremal problems in graph theory

Journal of Graph Theory, 1977
AbstractThe aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
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AN EXTREMAL PROBLEM IN GRAPH THEORY

The Quarterly Journal of Mathematics, 1980
Abbott, H. L., Hanson, D., Liu, A. C.
openaire   +1 more source

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.
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On an extremal inverse problem in the graph theory

Diskretnyi analiz i issledovanie operatsii, 2015
Dainiak, A. B., Kurnosov, A. D.
openaire   +1 more source