4 citations · 8 across the 18 of their papers we have counts for
5 papers · 1 filter
A proof of the Kim-Vu sandwich conjecture
Natalie Behague, Daniel Il'kovič, Richard Montgomery
In 2004, Kim and Vu conjectured that, when , the random -regular graph can be sandwiched with high probability between two random binomial graphs …
Nearly all known Euclidean Ramsey sets are subsoluble
Natalie Behague
A finite set in a Euclidean space is called Ramsey if for every there exists an integer such that whenever is coloured with colours, t…
Colour-biased Hamilton cycles in dense graphs and random graphs
Natalie Behague, Debsoumya Chakraborti, Jared León
A classical result of Dirac says that every -vertex graph with minimum degree at least contains a Hamilton cycle. A `discrepancy' version of Dirac's theorem was sh…
A case of the dijoin conjecture on inverting oriented graphs
Natalie Behague, Patrick Gaudart-Wifling
For an oriented graph , the inversion of in is the graph obtained by reversing the orientation of all arcs with both ends in . The inversion number $\ma…
Sabotaging Mantel's Theorem
Natalie Behague, Debsoumya Chakraborti, Xizhi Liu
One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph on vertices is $\lfloor n^2/4 \rflo…