4 citations · 9 across the 5 of their papers we have counts for
7 papers · 1 filter
Sparse Sets in Triangle-free Graphs
Tınaz Ekim, Burak Nur Erdem, John Gimbel
A set of vertices is -sparse if it induces a graph with a maximum degree of at most . In this missive, we consider the order of the largest -sparse set in a triangle-free…
Defective Ramsey Numbers in Graph Classes
Yunus Emre Demirci, Tınaz Ekim, John Gimbel +1
Given a graph , a -sparse -set is a set of vertices inducing a subgraph with maximum degree at most . A -dense -set is a set of vertices that is -spars…
Fractional cocoloring of graphs
John Gimbel, André Kündgen, Michael Molloy
The cochromatic number of a graph is the fewest number of colors needed to color the vertices of so that each color class is a clique or an independent set. In a fra…
Obstacle Numbers of Planar Graphs
John Gimbel, Patrice Ossona de Mendez, Pavel Valtr
Given finitely many connected polygonal obstacles in the plane and a set of points in general position and not in any obstacle, the {\em visibility graph} of $P…
Approximations of the domination number of a graph
Glenn G. Chappell, John Gimbel, Chris Hartman
Given a graph G, the domination number gamma(G) of G is the minimum order of a set S of vertices such that each vertex not in S is adjacent to some vertex in S. Equivalently, label…
Graphs with obstacle number greater than one
Leah Wrenn Berman, Glenn G. Chappell, Jill R. Faudree +3
An \emph{obstacle representation} of a graph is a straight-line drawing of in the plane together with a collection of connected subsets of the plane, called \emph{obstacles…
Covering line graphs with equivalence relations
L. Esperet, J. Gimbel, A. King
An equivalence graph is a disjoint union of cliques, and the equivalence number of a graph is the minimum number of equivalence subgraphs needed to cover the e…