Matthew Wales

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20192021

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math.CO2021

The extremal function for structured sparse minors

Matthew Wales

Let $c (H)$ be the smallest value for which $e (G) /∣ G ∣ \geq c (H)$ implies $H$ is a minor of $G$ . We show a new upper bound on $c (H)$ , which improves previous bounds for graphs with a…

math.CO2021

Bipartite clique minors in graphs of large Hadwiger number

Matthew Wales

The Hadwiger number $h (G)$ is the order of the largest complete minor in $G$ . Does sufficient Hadwiger number imply a minor with additional properties? In [2], Geelen et al showed…

math.CO2019

Distribution of colors in Gallai colorings

András Gyárfás, Dömötör Pálvölgyi, Balázs Patkós +1

A Gallai coloring is an edge coloring that avoids triangles colored with three different colors. Given integers $e_{1} \geq e_{2} \geq \dots \geq e_{k}$ with $\sum_{i = 1}^{k} e_{i} = (2 n)$ …