Ewan Davies

activity

20152023

most citedOn the average size of independent sets in triangle-free graphs

41 citations · 175 across the 19 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.CO2016★ 15 cited

Extremes of the internal energy of the Potts model on cubic graphs

Ewan Davies, Matthew Jenssen, Will Perkins +1

We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs…

math.CO2016★ 41 cited

On the average size of independent sets in triangle-free graphs

Ewan Davies, Matthew Jenssen, Will Perkins +1

We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$ , showing that an independent s…

math.CO2016★ 11 cited

Multicolour Ramsey numbers of paths and even cycles

Ewan Davies, Matthew Jenssen, Barnaby Roberts

We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that $(k - 1) n + o (n) \leq R_{k} (P_{n}) \leq R_{k} (C_{n}) \leq k n + o (n)$ . The upper bound was…