Results 61 to 70 of about 995,571 (241)
, 2014 Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete ...
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Extremal regular graphs of given chromatic number [PDF]
Ars Combinatoria-2023, 2019 We define an extremal $(r|\chi)$-graph as an $r$-regular graph with chromatic number $\chi$ of minimum order. We show that the Tur{\' a}n graphs $T_{ak,k}$, the antihole graphs and the graphs $K_k\times K_2$ are extremal in this sense. We also study extremal Cayley $(r|\chi)$-graphs and we exhibit several $(r|\chi)$-graph constructions arising from Tur{
arxiv +1 more source
Geometric variational problems of statistical mechanics and of combinatorics
, 2000 We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a ...
Alexander K. +9 more
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Extremal, enumerative and probabilistic results on ordered hypergraph matchings
Forum of Mathematics, SigmaAn ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders.
Michael Anastos +3 more
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On Lev's periodicity conjecture
Bulletin of the London Mathematical Society, EarlyView.Abstract We classify the sum‐free subsets of F3n${\mathbb {F}}_3^n$ whose density exceeds 16$\frac{1}{6}$. This yields a resolution of Vsevolod Lev's periodicity conjecture, which asserts that if a sum‐free subset A⊆F3n${A\subseteq {\mathbb {F}}_3^n}$ is maximal with respect to inclusion and aperiodic (in the sense that there is no non‐zero vector v$v$
Christian Reiher
wiley +1 more source
Additive energies on discrete cubes
Discrete Analysis, 2023 One definition of additive combinatorics is that it is the study of subsets of (usually Abelian) groups. Two much studied parameters associated with a subset $A$ are the size of its sumset $A+A=\{a+b:a,b\in A\}$ (or the product set $A.A=\{a.b:a,b\in A\}$
Jaume de Dios Pont +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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Effects of altitude and exercise intensity on cardiac function in rats
Experimental Physiology, EarlyView.Abstract High‐altitude exercise affects cardiac function. This study investigated how altitude and exercise intensity interacted to affect cardiac function of Sprague‐Dawley rats. Four altitudes (410, 3600, 4600 and 5600 m) and three exercise intensities (non‐exercise (N), low‐intensity exercise (L) and high‐intensity exercise (H)) were tested ...
Minxia Zhu +7 more
wiley +1 more source
Forbidden intersection problems for families of linear maps
Discrete Analysis, 2023 Forbidden intersection problems for families of linear maps, Discrete Analysis 2023:19, 32 pp. A central problem in extremal combinatorics is to determine the maximal size of a set system given constraints on the sizes of the sets in the system and on ...
David Ellis, Guy Kindler, Noam Lifshitz
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On the Turan number of forests [PDF]
, 2012 The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently ...
Lidický, Bernard +2 more
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