Christopher Cox

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20182021

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3 papers · 1 filter

math.CO2021

The maximum number of 10- and 12-cycles in a planar graph

Christopher Cox, Ryan R. Martin

For a fixed planar graph $H$ , let $N_{P} (n, H)$ denote the maximum number of copies of $H$ in an $n$ -vertex planar graph. In the case when $H$ is a…

math.CO2019

Restricted online Ramsey numbers of matchings and trees

Joseph Briggs, Christopher Cox

Consider a two-player game between players Builder and Painter. Painter begins the game by picking a coloring of the edges of $K_{n}$ , which is hidden from Builder. In each round, Bu…

math.CO2018

Nearly orthogonal vectors and small antipodal spherical codes

Boris Bukh, Christopher Cox

How can $d + k$ vectors in $R^{d}$ be arranged so that they are as close to orthogonal as possible? In particular, define $θ(d,k):=\min_X\max_{x\neq y\in X}|\langle x,y\rangle…