58 citations
- University of Missouri–St. LouisUS18 papers
- Lanzhou UniversityCN7 papers
- Tata Institute of Fundamental ResearchIN4 papers
- Hofstra UniversityUS3 papers
- Nanjing UniversityCN3 papers
- Stony Brook UniversityUS3 papers
- Australian National UniversityAU2 papers
- Centre National de la Recherche ScientifiqueFR2 papers
- Northeastern UniversityUS2 papers
- Simon Fraser UniversityCA2 papers
- Southern University of Science and TechnologyCN2 papers
- University of British ColumbiaCA2 papers
10 papers · 1 filter
On Mixed Cages
Geoffrey Exoo
Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper…
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…
The Hadwiger-Nelson problem with two forbidden distances
Geoffrey Exoo, Dan Ismailescu
In 1950 Edward Nelson asked the following simple-sounding question: \emph{How many colors are needed to color the Euclidean plane such that no two points distance $1…
Bounds for the smallest -chromatic graphs of given girth
Geoffrey Exoo, Jan Goedgebeur
Let denote the smallest order of a -chromatic graph of girth at least . We consider the problem of determining for small values of and . After giving…
The chromatic number of the plane is at least 5 - a new proof
Geoffrey Exoo, Dan Ismailescu
We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points unit distance apart which are identically colored.
New Lower Bounds for 28 Classical Ramsey Numbers
Geoffrey Exoo, Milos Tatarevic
We establish new lower bounds for classical two and three color Ramsey numbers, and describe the heuristic search procedures we used. Several of the new three color bounds are…