Katherine Staden

activity

20122024

most citedProof of Komlós's conjecture on Hamiltonian subsets

22 citations · 93 across the 17 of their papers we have counts for

collaborators

Showing 2017Show all

5 papers · 1 filter

math.CO2017★ 9 cited

The exact minimum number of triangles in graphs of given order and size

Hong Liu, Oleg Pikhurko, Katherine Staden

What is the minimum number of triangles in a graph of given order and size? Motivated by earlier results of Mantel and Turán, Rademacher solved the first non-trivial case of this p…

math.CO2017★ 3 cited

On the maximum number of integer colourings with forbidden monochromatic sums

Hong Liu, Maryam Sharifzadeh, Katherine Staden

Let $f (n, r)$ denote the maximum number of colourings of $A \subseteq {1, \dots, n}$ with $r$ colours such that each colour class is sum-free. Here, a sum is a subset $\…

math.CO2017

Minimum number of additive tuples in groups of prime order

Ostap Chervak, Oleg Pikhurko, Katherine Staden

For a prime number $p$ and a sequence of integers $a_{0}, \dots, a_{k} \in {0, 1, \dots, p}$ , let $s (a_{0}, \dots, a_{k})$ be the minimum number of $(k + 1)$ -tuples $(x_0,\dots,x_k)\in A_0\times\d…

math.CO2017★ 22 cited

Proof of Komlós's conjecture on Hamiltonian subsets

Jaehoon Kim, Hong Liu, Maryam Sharifzadeh +1

Komlós conjectured in 1981 that among all graphs with minimum degree at least $d$ , the complete graph $K_{d + 1}$ minimises the number of Hamiltonian subsets, where a subset of verti…

math.CO2017

Independent sets in hypergraphs and Ramsey properties of graphs and the integers

Robert Hancock, Katherine Staden, Andrew Treglown

Many important problems in combinatorics and other related areas can be phrased in the language of independent sets in hypergraphs. Recently Balogh, Morris and Samotij, and indepen…