Results 1 to 10 of about 34,294 (314)
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
doaj +5 more sources
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
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.
Igal Sason
doaj +4 more sources
Extremal graph theory and finite forcibility [PDF]
Electronic Notes in Discrete Mathematics, 2017 We study the uniqueness of optimal solutions to extremal graph theory problems. Our main result is a counterexample to the following conjecture of Lov´asz, which is often referred to as saying that “every extremal graph theory problem has a finitely ...
Grzesik, Andrzej +2 more
core +4 more sources
Guessing Numbers and Extremal Graph Theory [PDF]
The Electronic Journal of Combinatorics, 2022 For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the colors of the vertices in its neighborhood.
Jo Ryder Martin, Puck Rombach
openalex +4 more sources
Extremal infinite graph theory
Discrete Mathematics, 2011 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. Many open problems are suggested.
Maya Stein
openalex +6 more sources
Graph Theory and Qubit Information Systems of Extremal Black Branes [PDF]
, 2014 Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain extremal black ...
Belhaj, Adil +2 more
core +2 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
openalex +3 more sources
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
openalex +3 more sources
Extremal Graph Theory for Metric Dimension and Diameter [PDF]
Electronic Notes in Discrete Mathematics, 2007 A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}
C. Hern +5 more
core +7 more sources
Problems in extremal graph theory [PDF]
, 2010 We consider a variety of problems in extremal graph and set theory. The {\em chromatic number} of $G$, $\chi(G)$, is the smallest integer $k$ such that $G$ is $k$-colorable.
Ozkahya, Lale
core +2 more sources