Barnaby Roberts

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20152018

most citedPartite Saturation Problems

1 citations · 1 across the 1 of their papers we have counts for

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math.CO2018

The multicolour size-Ramsey number of powers of paths

Jie Han, Matthew Jenssen, Yoshiharu Kohayakawa +2

Given a positive integer $s$ , a graph $G$ is $s$ -Ramsey for a graph $H$ , denoted $G \to (H)_{s}$ , if every $s$ -colouring of the edges of $G$ contains a monochromatic copy of $…

math.CO2017

The size-Ramsey number of powers of paths

Dennis Clemens, Matthew Jenssen, Yoshiharu Kohayakawa +4

Given graphs $G$ and $H$ and a positive integer $q$ say that $G$ is $q$ -Ramsey for $H$ , denoted $G \to (H)_{q}$ , if every $q$ -colouring of the edges of $G$ contains a monochro…

math.CO2016

Ramsey Numbers of Connected Clique Matchings

Barnaby Roberts

We determine the Ramsey number of a connected clique matching. That is, we show that if $G$ is a $2$ -edge-coloured complete graph on $(r^{2} - r - 1) n - r + 1$ vertices, then there i…

math.CO2015★ 1 cited

Partite Saturation Problems

Barnaby Roberts

We look at several saturation problems in complete balanced blow-ups of graphs. We let $H [n]$ denote the blow-up of $H$ onto parts of size $n$ and refer to a copy of $H$ in $H [n]$ …