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pro vyhledávání: '"Glock, Stefan"'
Let $f^{(r)}(n;s,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no subgraph with $k$ edges and at most $s$ vertices. Brown, Erd\H{o}s and S\'os [New directions in the theory of graphs (Proc. Third Ann Arbor
Externí odkaz:
http://arxiv.org/abs/2403.04474
In this paper, we initiate the study of discrepancy questions for spanning subgraphs of $k$-uniform hypergraphs. Our main result is that any $2$-colouring of the edges of a $k$-uniform $n$-vertex hypergraph $G$ with minimum $(k-1)$-degree $\delta(G)
Externí odkaz:
http://arxiv.org/abs/2312.09976
In his seminal 1976 paper, P\'osa showed that for all $p\geq C\log n/n$, the binomial random graph $G(n,p)$ is with high probability Hamiltonian. This leads to the following natural questions, which have been extensively studied: How well is it typic
Externí odkaz:
http://arxiv.org/abs/2310.11580
Finding general conditions which ensure that a graph is Hamiltonian is a central topic in graph theory. An old and well known conjecture in the area states that any $d$-regular $n$-vertex graph $G$ whose second largest eigenvalue in absolute value $\
Externí odkaz:
http://arxiv.org/abs/2303.05356
Let $f^{(r)}(n;s,k)$ be the maximum number of edges of an $r$-uniform hypergraph on $n$ vertices not containing a subgraph with $k$ edges and at most $s$ vertices. In 1973, Brown, Erd\H{o}s and S\'os conjectured that the limit $$\lim_{n\to \infty} n^
Externí odkaz:
http://arxiv.org/abs/2209.14177
A celebrated theorem of Pippenger, and Frankl and R\"odl states that every almost-regular, uniform hypergraph $\mathcal{H}$ with small maximum codegree has an almost-perfect matching. We extend this result by obtaining a ``conflict-free'' matching, w
Externí odkaz:
http://arxiv.org/abs/2205.05564
Autor:
Glock, Stefan1 (AUTHOR), Joos, Felix2 (AUTHOR), Kim, Jaehoon3 (AUTHOR), Kühn, Marcus2 (AUTHOR), Lichev, Lyuben4 (AUTHOR), Pikhurko, Oleg5 (AUTHOR)
Publikováno v:
Proceedings of the American Mathematical Society, Series B. 6/4/2024, Vol. 11, p173-186. 14p.
Publikováno v:
In Advances in Mathematics December 2024 458 Part B
An $n$-queens configuration is a placement of $n$ mutually non-attacking queens on an $n\times n$ chessboard. The $n$-queens completion problem, introduced by Nauck in 1850, is to decide whether a given partial configuration can be completed to an $n
Externí odkaz:
http://arxiv.org/abs/2111.11402
We present a modification of the Depth first search algorithm, suited for finding long induced paths. We use it to give simple proofs of the following results. We show that the induced size-Ramsey number of paths satisfies $\hat{R}_{\mathrm{ind}}(P_n
Externí odkaz:
http://arxiv.org/abs/2106.08975