Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Bucic, Matija"'
Autor:
Balla, Igor, Bucić, Matija
A family of lines passing through the origin in an inner product space is said to be equiangular if every pair of lines defines the same angle. In 1973, Lemmens and Seidel raised what has since become a central question in the study of equiangular li
Externí odkaz:
http://arxiv.org/abs/2409.16219
An $\ell$-lift of a graph $G$ is any graph obtained by replacing every vertex of $G$ with an independent set of size $\ell$, and connecting every pair of two such independent sets that correspond to an edge in $G$ by a matching of size $\ell$. Graph
Externí odkaz:
http://arxiv.org/abs/2407.10565
Counting independent sets in graphs and hypergraphs under a variety of restrictions is a classical question with a long history. It is the subject of the celebrated container method which found numerous spectacular applications over the years. We con
Externí odkaz:
http://arxiv.org/abs/2406.07799
It is well-known that polynomial versions of theorems of R\"odl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erd\H{o}s-Hajnal conjecture. In this note, we prove that these three conjectures are in
Externí odkaz:
http://arxiv.org/abs/2403.08303
Autor:
Bucić, Matija, Davies, James
In 1975 Erd\H{o}s initiated the study of the following very natural question. What can be said about the chromatic number of unit distance graphs in $\mathbb{R}^2$ that have large girth? Over the years this question and its natural extension to $\mat
Externí odkaz:
http://arxiv.org/abs/2312.06898
Publikováno v:
Advances in Combinatorics 2024:5, 16pp
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rz\k{a}\.zewski, Thomass\'e, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains eithe
Externí odkaz:
http://arxiv.org/abs/2311.03341
An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a
Externí odkaz:
http://arxiv.org/abs/2309.04460
A classical problem, due to Gerencs\'er and Gy\'arf\'as from 1967, asks how large a monochromatic connected component can we guarantee in any $r$-edge colouring of $K_n$? We consider how big a connected component can we guarantee in any $r$-edge colo
Externí odkaz:
http://arxiv.org/abs/2308.15387
Erd\H{o}s' unit distance problem and Erd\H{o}s' distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum number of unit distances, or the minimum number of distinct distanc
Externí odkaz:
http://arxiv.org/abs/2302.09058
In 1977, Erd\H{o}s and Hajnal made the conjecture that, for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^c$; and they proved that this is true with $ |G|^c$ replaced by $2^{c\
Externí odkaz:
http://arxiv.org/abs/2301.10147