4 papers · 1 filter
On oriented cycles in randomly perturbed digraphs
Igor Araujo, József Balogh, Robert A. Krueger +2
In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every , there exists a constant such…
Rainbow Connection for Complete Multipartite Graphs
Igor Araujo, Kareem Benaissa, Richard Bi +3
A path in an edge-colored graph is said to be rainbow if no color repeats on it. An edge-colored graph is said to be rainbow -connected if every pair of vertices is connected by…
New Lower Bounds For Essential Covers Of The Cube
Igor Araujo, József Balogh, Letícia Mattos
An essential cover of the vertices of the -cube by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of a…
On the Maximum -free Subhypergraphs of a Random Hypergraph
Igor Araujo, József Balogh, Haoran Luo
Denote by the -uniform hypergraph on vertex set with hyperedges . Balogh, Butterfield, Hu, and Lenz proved that if for…