58 citations · 220 across the 56 of their papers we have counts for
6 papers · 1 filter
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…
On the maximum number of integer colourings with forbidden monochromatic sums
Hong Liu, Maryam Sharifzadeh, Katherine Staden
Let denote the maximum number of colourings of with colours such that each colour class is sum-free. Here, a sum is a subset $\…
Stability and exact Turan numbers for matroids
Hong Liu, Sammy Luo, Peter Nelson +1
We consider the Turán-type problem of bounding the size of a set that does not contain a linear copy of a given fixed set ,…
Edges not in any monochromatic copy of a fixed graph
Hong Liu, Oleg Pikhurko, Maryam Sharifzadeh
For a sequence of graphs, let denote the maximum number of edges not contained in any monochromatic copy of in colour , f…
Rainbow spanning trees in properly coloured complete graphs
József Balogh, Hong Liu, Richard Montgomery
In this short note, we study pairwise edge-disjoint rainbow spanning trees in properly edge-coloured complete graphs, where a graph is rainbow if its edges have distinct colours. B…
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 , the complete graph minimises the number of Hamiltonian subsets, where a subset of verti…