Results 21 to 30 of about 24,841 (222)
A proof of the stability of extremal graphs, Simonovits' stability from Szemer\'edi's regularity [PDF]
, 2015 The following sharpening of Tur\'an's theorem is proved. Let $T_{n,p}$ denote the complete $p$--partite graph of order $n$ having the maximum number of edges. If $G$ is an $n$-vertex $K_{p+1}$-free graph with $e(T_{n,p})-t$ edges then there exists an (at
Füredi, Zoltán
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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
Erdös, P., Simonovits, M.
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Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets [PDF]
, 2012 An identifying code of a (di)graph $G$ is a dominating subset $C$ of the vertices of $G$ such that all distinct vertices of $G$ have distinct (in)neighbourhoods within $C$.
A. Winter +15 more
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A Survey of Maximal k-Degenerate Graphs and k-Trees
Theory and Applications of GraphsThis article surveys results on maximal $k$-degenerate graphs, $k$-trees, and related classes including simple $k$-trees, $k$-paths, maximal outerplanar graphs, and Apollonian networks.
Allan Bickle
doaj +1 more source
Optimal transportation, topology and uniqueness [PDF]
, 2010 The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing the goods to be
Ahmad, Najma +2 more
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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
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 ...
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FEBS Open Bio, EarlyView.This protocol paper outlines methods to establish the success of a time‐resolved serial crystallographic experiment, by means of statistical analysis of timepoint data in reciprocal space and models in real space. We show how to amplify the signal from excited states to visualise structural changes in successful experiments.
Jake Hill +4 more
wiley +1 more source
Weighted Asymmetry Index: A New Graph-Theoretic Measure for Network Analysis and Optimization
MathematicsGraph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures.
Ali N. A. Koam +3 more
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On some extremal problems in graph theory
, 1999 In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to one in analysis. We study both weighted and unweighted graphs which are extremal for these invariants.
Jakobson, Dmitry, Rivin, Igor
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