Results 51 to 60 of about 58,072 (195)
On the number of pentagons in triangle-free graphs [PDF]
, 2013 Using the formalism of flag algebras, we prove that every triangle-free graph G with n vertices contains at most (n/5)(5) cycles of length five. Moreover, the equality is attained only when n is divisible by five and G is the balanced blow-up of the ...
Hatami, Hamed +4 more
core +1 more source
Several Problems in Extremal Combinatorics [PDF]
, 2014 Extremal combinatorics is one of the central branches of discrete mathematics. It focuses on determining or estimating the optimal possible size of a discrete structure(e.g. set systems, graphs) with certain properties.
Gan, Wenying
core +1 more source
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
doaj +1 more source
Simple juntas for shifted families
Discrete Analysis, 2020 **For the moment the link is to the submitted version of the article. It will be updated when the final version has been posted to arXiv.** Simple juntas for shifted families, Discrete Analysis 2020:14, 18 pp.
Peter Frankl, Andrey Kupavskii
doaj +1 more source
How to pick your football team
Mathematika, Volume 72, Issue 4, October 2026.Abstract Team captains Alice and Bob divide up 2m$2m$ footballers, each reduced to a real‐valued score, into two teams of m$m$ footballers each. On each turn, one captain plays picker, and the other chooser: the picker names a footballer yet to be selected, and the chooser decides which captain's team receives that footballer.
Bhargav Narayanan
wiley +1 more source
Machine Learning for Synthetic Organic Chemistry: Methods, Applications, and Best Practices
Angewandte Chemie Novit, Volume 2, Issue 3, September 2026.Artificial intelligence (AI) and machine learning (ML) are increasingly reshaping experimental chemistry. This review maps the challenges of synthetic organic chemistry to modern digital tools that can help address them. While focusing on the practical application of ML tools in real‐world laboratory settings, we outline prerequisites, emerging ...
Niklas Hölter +3 more
wiley +1 more source
On the number of $\mathcal {H}$ -free hypergraphs
Forum of Mathematics, SigmaTwo central problems in extremal combinatorics are concerned with estimating the number $\mathrm {ex}(n,\mathcal {H})$ , the size of the largest $\mathcal {H}$ -free hypergraph on n vertices, and the number $\mathrm {forb}(n,\mathcal {H})$
Tao Jiang, Sean Longbrake
doaj +1 more source
Hypergraph removal lemmas via robust sharp threshold theorems
Discrete Analysis, 2020 Hypergraph removal lemmas via robust sharp threshold theorems, Discrete Analysis 2020:10, 46 pp. A central result in additive and extremal combinatorics is the triangle removal lemma, which roughly speaking states that a graph with few triangles can be ...
Noam Lifshitz
doaj +1 more source
Critical‐Network Lesion‐Symptom Mapping
Human Brain Mapping, Volume 47, Issue 13, September 2026.We introduce Critical‐Network Lesion‐Symptom Mapping (CN‐LSM), an atlas‐based approach that uses ensemble modeling and out‐of‐sample prediction to identify brain networks supporting behavior in stroke patients. CN‐LSM outperforms standard multivariate methods in ground‐truth recovery while delivering interpretable, low‐dimensional results with fewer ...
Grant M. Walker +6 more
wiley +1 more source
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, Volume 113, Issue 1, Page 88-96, September 2026.ABSTRACT Chvátal showed that for any tree T with k edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1. For r = 3 or 4, we show that, if T is an r‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ). The 3‐uniform result comes from observing a construction of Cooper and Mubayi.
Jiaxi Nie
wiley +1 more source