13 citations · 73 across the 38 of their papers we have counts for
7 papers · 1 filter
On triangular biregular degree sequences
Benjamin Egan, Yuri Nikolayevsky
A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 ha…
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…
On planar bipartite biregular degree sequences
Patrick Adams, Yuri Nikolayevsky
A pair of sequences of natural numbers is called planar if there exists a simple, bipartite, planar graph for which the given sequences are the degree sequences of its parts. For a…
Annular and pants thrackles
Grace Misereh, Yuri Nikolayevsky
A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of a graph on the plane cannot hav…
Thrackles containing a standard musquash
Grace Misereh, Yuri Nikolayevsky
A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a planar thrackle drawing of a graph cannot have more…
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.