4 citations · 22 across the 15 of their papers we have counts for
16 papers
New small regular graphs of given girth: the cage problem and beyond
Geoffrey Exoo, Jan Goedgebeur, Jorik Jooken +2
The cage problem concerns finding -graphs, which are -regular graphs with girth , of the smallest possible number of vertices. The central goal is to determine $n(k,g)…
A Lower Bound for R(5,6)
Geoffrey Exoo
The known lower bound for the the classical Ramsey number is improved from to . The method used to construct the graph is a simple variant of computational method…
Attainable bounds for algebraic connectivity and maximally-connected regular graphs
Geoffrey Exoo, Theodore Kolokolnikov, Jeanette Janssen +1
We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Bop…
On large regular (1,1,k)-mixed graphs
C. Dalfó, G. Erskine, G. Exoo +4
An -mixed graph has every vertex with undirected degree , directed in- and out-degree , and diameter . In this paper, we study the case , proposing som…
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…
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 Mixed Graph Achieving A Moore-like Bound
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 we construct a mixed cage of o…
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…
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…
On the Chromatic Number of for Small Values of
Geoffrey Exoo, Dan Ismailescu
The lower bound for the chromatic number of is improved for $n = 6, 7, 10, 11, 12, 13 \mbox{ and } 14$.
Three Graphs and the Erdős-Gyárfás Conjecture
Geoffrey Exoo
Three graphs related to the \EGC\, are presented. The graphs are derived from the Buckyball, the Petersen graph, and the Tutte-Coxeter graph. The first graph is a partial answer to…
Computational determination of (3,11) and (4,7) cages
Geoffrey Exoo, Brendan D. McKay, Wendy Myrvold +1
A (k,g)-graph is a k-regular graph of girth g, and a (k,g)-cage is a (k,g)-graph of minimum order. We show that a (3,11)-graph of order 112 found by Balaban in 1973 is minimal and…