Ryan R. Martin

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20242026

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math.CO2026

Ramsey numbers of multiple copies of a graph and the random Ramsey theorem

Andrea Freschi, Ryan R. Martin, Andrew Treglown

A well-known result of Burr, Erdős and Spencer [Transactions of the American Mathematical Society, 1975] determines the $2$ -colour Ramsey number for any sufficiently large collecti…

math.CO2026

The edit distance of word-representable and comparability graphs

Sergey Kitaev, Ryan R. Martin

In this paper, we establish that the maximum edit distance of an $n$ -vertex graph from the hereditary property of word-representable graphs is $n^{2} /8 - o (n^{2})$ . In addition, we estab…