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pro vyhledávání: '"Marciano, João Pedro"'
Autor:
Hàn, Hiêp, Lang, Richard, Marciano, João Pedro, Pavez-Signé, Matías, Sanhueza-Matamala, Nicolás, Treglown, Andrew, Zárate-Guerén, Camila
We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main result solves this problem for perfect matchings under minimum degree c
Externí odkaz:
http://arxiv.org/abs/2408.11016
The Cayley sum graph $\Gamma_A$ of a set $A \subseteq \mathbb{Z}_n$ is defined to have vertex set $\mathbb{Z}_n$ and an edge between two distinct vertices $x, y \in \mathbb{Z}_n$ if $x + y \in A$. Green and Morris proved that if the set $A$ is a $p$-
Externí odkaz:
http://arxiv.org/abs/2406.09361
A classical result of Chv\'atal implies that if $n \geq (r-1)(t-1) +1$, then any colouring of the edges of $K_n$ in red and blue contains either a monochromatic red $K_r$ or a monochromatic blue $P_t$. We study a natural generalization of his result,
Externí odkaz:
http://arxiv.org/abs/2403.13742
The $n$-dimensional hypercube $Q_n$ is a graph with vertex set $\{0,1\}^n$ and there is an edge between two vertices if they differ in exactly one coordinate. For any graph $H$, define $\text{ex}(Q_n,H)$ to be the maximum number of edges of a subgrap
Externí odkaz:
http://arxiv.org/abs/2402.19409
Publikováno v:
European J. Combin. 124 (2025) 104078
The $n$-dimensional random twisted hypercube $\mathbf{G}_n$ is constructed recursively by taking two instances of $\mathbf{G}_{n-1}$, with any joint distribution, and adding a random perfect matching between their vertex sets. Benjamini, Dikstein, Gr
Externí odkaz:
http://arxiv.org/abs/2306.01728
Deciding whether a graph can be edge-decomposed into a matching and a $k$-bounded linear forest was recently shown by Campbell, H{\"o}rsch and Moore to be NP-complete for every $k \ge 9$, and solvable in polynomial time for $k=1,2$. In the first part
Externí odkaz:
http://arxiv.org/abs/2304.03256
The set-colouring Ramsey number $R_{r,s}(k)$ is defined to be the minimum $n$ such that if each edge of the complete graph $K_n$ is assigned a set of $s$ colours from $\{1,\ldots,r\}$, then one of the colours contains a monochromatic clique of size $
Externí odkaz:
http://arxiv.org/abs/2212.06802
Akademický článek
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Publikováno v:
Random Structures & Algorithms; Mar2024, Vol. 64 Issue 2, p157-169, 13p
Akademický článek
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