Zobrazeno 1 - 10
of 436
pro vyhledávání: '"Felix, Christian"'
Autor:
Clemen, Felix Christian
Many problems in extremal combinatorics can be reduced to determining the independence number of a specific auxiliary hypergraph. We present two such problems, one from discrete geometry and one from hypergraph Tur\'an theory. Using results on hyperg
Externí odkaz:
http://arxiv.org/abs/2406.01499
Autor:
Clemen, Felix Christian, Kaiser, Peter
The billiard table is modeled as an $n$-dimensional box $[0,a_1]\times [0,a_2]\times \ldots \times [0,a_n] \subset \mathbb{R}^n$, with each side having real-valued lengths $a_i$ that are pairwise commensurable. A ball is launched from the origin in d
Externí odkaz:
http://arxiv.org/abs/2406.01119
Let $X$ be an $n$-element point set in the $k$-dimensional unit cube $[0,1]^k$ where $k \geq 2$. According to an old result of Bollob\'as and Meir (1992), there exists a cycle (tour) $x_1, x_2, \ldots, x_n$ through the $n$ points, such that $\left(\s
Externí odkaz:
http://arxiv.org/abs/2310.02839
Autor:
Jens E. Pedersen, Steven Abreu, Matthias Jobst, Gregor Lenz, Vittorio Fra, Felix Christian Bauer, Dylan Richard Muir, Peng Zhou, Bernhard Vogginger, Kade Heckel, Gianvito Urgese, Sadasivan Shankar, Terrence C. Stewart, Sadique Sheik, Jason K. Eshraghian
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-15 (2024)
Abstract Spiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation
Externí odkaz:
https://doaj.org/article/31b61ff6c22042c0a55ec54f03b8f39b
Almost $50$ years ago Erd\H{o}s and Purdy asked the following question: Given $n$ points in the plane, how many triangles can be approximate congruent to equilateral triangles? They pointed out that by dividing the points evenly into three small clus
Externí odkaz:
http://arxiv.org/abs/2303.14663
A balanced edge-coloring of the complete graph is an edge-coloring such that every vertex is incident to each color the same number of times. In this short note, we present a construction of a balanced edge-coloring with six colors of the complete gr
Externí odkaz:
http://arxiv.org/abs/2303.15476
An ordered graph is a graph with a linear ordering on its vertices. The online Ramsey game for ordered graphs $G$ and $H$ is played on an infinite sequence of vertices; on each turn, Builder draws an edge between two vertices, and Painter colors it r
Externí odkaz:
http://arxiv.org/abs/2210.05235
An edge-coloring of a complete graph with a set of colors $C$ is called completely balanced if any vertex is incident to the same number of edges of each color from $C$. Erd\H{o}s and Tuza asked in $1993$ whether for any graph $F$ on $\ell$ edges and
Externí odkaz:
http://arxiv.org/abs/2209.13867
Erd\H{o}s, F\"uredi, Rothschild and S\'os initiated a study of classes of graphs that forbid every induced subgraph on a given number $m$ of vertices and number $f$ of edges. Extending their notation to $r$-graphs, we write $(n,e) \to_r (m,f)$ if eve
Externí odkaz:
http://arxiv.org/abs/2208.06626
For every integer $t \ge 0$, denote by $F_5^t$ the hypergraph on vertex set $\{1,2,\ldots, 5+t\}$ with hyperedges $\{123,124\} \cup \{34k : 5 \le k \le 5+t\}$. We determine $\mathrm{ex}(n,F_5^t)$ for every $t\ge 0$ and sufficiently large $n$ and char
Externí odkaz:
http://arxiv.org/abs/2208.00652