Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Roberts, Barnaby"'
The square $G^2$ of a graph $G$ is the graph on $V(G)$ with a pair of vertices $uv$ an edge whenever $u$ and $v$ have distance $1$ or $2$ in $G$. Given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum $N$ such that whenever the edges of
Externí odkaz:
http://arxiv.org/abs/2212.14860
Autor:
Allen, Peter, Böttcher, Julia, Corsten, Jan, Davies, Ewan, Jenssen, Matthew, Morris, Patrick, Roberts, Barnaby, Skokan, Jozef
For a graph $G$ and $p\in[0,1]$, we denote by $G_p$ the random sparsification of $G$ obtained by keeping each edge of $G$ independently, with probability $p$. We show that there exists a $C>0$ such that if $p\geq C(\log n)^{1/3}n^{-2/3}$ and $G$ is a
Externí odkaz:
http://arxiv.org/abs/2209.01116
Publikováno v:
In Journal of Great Lakes Research June 2024 50(3)
Akademický článek
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Autor:
Han, Jie, Jenssen, Matthew, Kohayakawa, Yoshiharu, Mota, Guilherme Oliveira, Roberts, Barnaby
Given a positive integer $s$, a graph $G$ is $s$-Ramsey for a graph $H$, denoted $G\rightarrow (H)_s$, if every $s$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The $s$-colour size-Ramsey number ${\hat{r}}_s(H)$ of a graph $H$
Externí odkaz:
http://arxiv.org/abs/1811.00844
Autor:
Clemens, Dennis, Jenssen, Matthew, Kohayakawa, Yoshiharu, Morrison, Natasha, Mota, Guilherme Oliveira, Reding, Damian, Roberts, Barnaby
Given graphs $G$ and $H$ and a positive integer $q$ say that $G$ is $q$-Ramsey for $H$, denoted $G\rightarrow (H)_q$, if every $q$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The size-Ramsey number $\hat{r}(H)$ of a graph $H$
Externí odkaz:
http://arxiv.org/abs/1707.04297
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model and monomer-
Externí odkaz:
http://arxiv.org/abs/1704.07784
Autor:
Allen, Peter, Böttcher, Julia, Corsten, Jan, Davies, Ewan, Jenssen, Matthew, Morris, Patrick, Roberts, Barnaby, Skokan, Jozef
Publikováno v:
Random Structures & Algorithms; Aug2024, Vol. 65 Issue 1, p61-130, 70p
Akademický článek
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Autor:
Thomas, Stephen1 (AUTHOR) stephen.thomas@nhsbt.nhs.uk, Roberts, Barnaby2 (AUTHOR), Domanović, Dragoslav3 (AUTHOR), Kramer, Koen4 (AUTHOR), Klochkov, Denis5 (AUTHOR), Sivasubramaniyam, Sujan6 (AUTHOR), Miloslavich, Dana7 (AUTHOR), Plançon, Jean‐Philippe8 (AUTHOR), Rossi, Françoise9 (AUTHOR), Misztela, Dominika10 (AUTHOR), Kirkpatrick, Lauren11 (AUTHOR), Miflin, Gail12 (AUTHOR), Birchall, Janet13 (AUTHOR), McLintock, Lorna14 (AUTHOR), Knight, Richard15 (AUTHOR)
Publikováno v:
Vox Sanguinis. May2023, Vol. 118 Issue 5, p345-353. 9p. 1 Graph.