Clayton Mizgerd

collaborators

2 papers

cs.DS2024

Rapid mixing of the down-up walk on matchings of a fixed size

Vishesh Jain, Clayton Mizgerd

Let $G = (V, E)$ be a graph on $n$ vertices and let $m^{*} (G)$ denote the size of a maximum matching in $G$ . We show that for any $I^´ > 0$ and for any $1 \leq k \leq (1 - I^´) m^{*} (G)$ , the…

math.CO2024

Inducibility of rainbow graphs

Emily Cairncross, Clayton Mizgerd, Dhruv Mubayi

Fix $k \geq 11$ and a rainbow $k$ -clique $R$ . We prove that the inducibility of $R$ is $k! / (k^{k} - k)$ . An extremal construction is a balanced recursive blow-up of $R$ . This answers a q…