11 citations · 23 across the 23 of their papers we have counts for
10 papers · 1 filter
Following in Yiu's Footsteps but on the Eisenstein Lattice
Christian Aebi, Grant Cairns
Paul Yiu proved that all Heron triangles are realizable on the integer lattice. We give an analogous result for triangles with vertices on the Eisenstein lattice.
Bad drawings of small complete graphs
Grant Cairns, Emily Groves, Yuri Nikolayevsky
We show that for (resp.~ ) there is a drawing with independent crossings, and no pair of independent edges cross more than once, provided is odd with $1\le i…
Equitable Candy Sharing
Grant Cairns
Children, sitting in a circle, each have a nonnegative number of candies in front of them. A whistle is blown and each child with more than one candy passes one candy to the left a…
A sufficient condition for a pair of sequences to be bipartite graphic
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
We present a sufficient condition for a pair of finite integer sequences to be degree sequences of a bipartite graph, based only on the lengths of the sequences and their largest a…
Spherical Thrackles
Grant Cairns, Timothy J. Koussas, Yuri Nikolayevsky
We establish Conway's thrackle conjecture in the case of spherical thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.
A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree lis…