Zobrazeno 1 - 10
of 563
pro vyhledávání: '"A. Behague"'
The semi-random hypergraph process is a natural generalisation of the semi-random graph process, which can be thought of as a one player game. For fixed $r < s$, starting with an empty hypergraph on $n$ vertices, in each round a set of $r$ vertices $
Externí odkaz:
http://arxiv.org/abs/2409.19335
A subgraph of the $n$-dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of arbitrarily large girth that are not layered. This answers a question of
Externí odkaz:
http://arxiv.org/abs/2404.18014
For an oriented graph $D$ and a set $X\subseteq V(D)$, the inversion of $X$ in $D$ is the graph obtained from $D$ by reversing the orientation of each edge that has both endpoints in $X$. Define the inversion number of $D$, denoted $inv(D)$, to be th
Externí odkaz:
http://arxiv.org/abs/2404.10663
For any fixed $d\geq1$ and subset $X$ of $\mathbb{N}^d$, let $r_X(n)$ be the maximum cardinality of a subset $A$ of $\{1,\dots,n\}^d$ which does not contain a subset of the form $\vec{b} + rX$ for $r>0$ and $\vec{b} \in \mathbb{R}^d$. Such a set $A$
Externí odkaz:
http://arxiv.org/abs/2311.13709
Autor:
Baber, Rahil, Behague, Natalie, Calbet, Asier, Ellis, David, Erde, Joshua, Gray, Ron, Ivan, Maria-Romina, Janzer, Barnabás, Johnson, Robert, Milićević, Luka, Talbot, John, Tan, Ta Sheng, Wickes, Belinda
One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems in combinatorics has been put together by a subset of his former PhD s
Externí odkaz:
http://arxiv.org/abs/2310.18163
A graph $H$ is common if the limit as $n\to\infty$ of the minimum density of monochromatic labelled copies of $H$ in an edge colouring of $K_n$ with red and blue is attained by a sequence of quasirandom colourings. We apply an information-theoretic a
Externí odkaz:
http://arxiv.org/abs/2307.03788
Given two non-empty graphs $H$ and $T$, write $H\succcurlyeq T$ to mean that $t(H,G)^{|E(T)|}\geq t(T,G)^{|E(H)|}$ for every graph $G$, where $t(\cdot,\cdot)$ is the homomorphism density function. We obtain various necessary and sufficient conditions
Externí odkaz:
http://arxiv.org/abs/2305.16542
A collection of families $(\mathcal{F}_{1}, \mathcal{F}_{2} , \cdots , \mathcal{F}_{k}) \in \mathcal{P}([n])^k$ is cross-Sperner if there is no pair $i \not= j$ for which some $F_i \in \mathcal{F}_i$ is comparable to some $F_j \in \mathcal{F}_j$. Two
Externí odkaz:
http://arxiv.org/abs/2302.02516
Given a graph $H$, we say that an edge-coloured graph $G$ is $H$-rainbow saturated if it does not contain a rainbow copy of $H$, but the addition of any non-edge in any colour creates a rainbow copy of $H$. The rainbow saturation number $\text{rsat}(
Externí odkaz:
http://arxiv.org/abs/2211.08589
A graph $H$ is said to be common if the number of monochromatic labelled copies of $H$ in a red/blue edge colouring of a large complete graph is asymptotically minimized by a random colouring with an equal proportion of each colour. We extend this no
Externí odkaz:
http://arxiv.org/abs/2208.02045