4 citations · 14 across the 16 of their papers we have counts for
9 papers · 1 filter
A 5-chromatic same-distance graph in the hyperbolic plane
Geoffrey Exoo, Dan Ismailescu
The chromatic number of the plane problem asks for the minimum number of colors so that each point of the plane can be assigned a single color with the property that no two points…
The chromatic number of the Minkowski plane -- the regular polygon case
Geoffrey Exoo, David Fisher, Dan Ismailescu
The Hadwiger-Nelson problem asks for the minimum number of colors, so that each point of the plane can be assigned a single color with the property that no two points unit-distance…
On the maximum area of inscribed polygons
Dan Ismailescu, Min Jung Kim, Eric Wang
Given a convex -gon and a positive integer such that , let denote the largest area convex -gon contained in . We are interested in the minimum v…
An improved upper bound for the size of the sphere of influence graph
Dan Ismailescu, Sung Hoon Kim, Taeyang David Park
Let be a set of points in the plane. For each , let be the closed circular disk centered at with radius equal to the distance from to its closest neig…
Outdegree conditions forcing short cycles in digraphs
Dan Ismailescu, Joonsoo Lee, Andrew Yang
Given a positive integer , let be the smallest positive constant with the following property: \emph{ Every simple directed graph on vertices all whose outd…
A -chromatic two-distance graph in the plane
Geoffrey Exoo, Dan Ismailescu
We prove that if one colors each point of the Euclidean plane with one of five colors, then there exist two points of the same color that are either distance or distance ap…