26 citations · 51 across the 5 of their papers we have counts for
6 papers
Angle Covers: Algorithms and Complexity
William Evans, Ellen Gethner, Jack Spalding-Jamieson +1
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of cons…
Crossing numbers of complete tripartite and balanced complete multipartite graphs
Ellen Gethner, Leslie Hogben, Bernard Lidický +3
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar drawing of G. The rectilinear crossing number cr'(G) of G is the minimum number…
Extending Precolorings to Distinguish Group Actions
Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2
Given a group acting on a set , a -coloring of is distinguishing with respect to if the only that fixes is the identity action.…
List Distinguishing Parameters of Trees
Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2
A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D…
Toward the Rectilinear Crossing Number of : New Drawings, Upper Bounds, and Asymptotics
Alex Brodsky, Stephane Durocher, Ellen Gethner
Scheinerman and Wilf (1994) assert that `an important open problem in the study of graph embeddings is to determine the rectilinear crossing number of the complete graph K_n.' A re…
The Rectilinear Crossing Number of K_10 is 62
Alex Brodsky, Stephane Durocher, Ellen Gethner
A drawing of a graph G in the plane is said to be a rectilinear drawing of G if the edges are required to be line segments (as opposed to Jordan curves). We assume no three vertice…