12 citations · 13 across the 5 of their papers we have counts for
5 papers · 2 filters
Zero Forcing Number of Random Regular Graphs
Deepak Bal, Patrick Bennett, Sean English +2
The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become…
Large triangle packings and Tuza's conjecture in sparse random graphs
Patrick Bennett, Andrzej Dudek, Shira Zerbib
The triangle packing number of a graph is the maximum size of a set of edge-disjoint triangles in . Tuza conjectured that in any graph there exists a set of at mo…
Weighted Turan Problems with Applications
Patrick Bennett, Sean English, Maria Talanda-Fisher
Suppose the edges of are assigned weights by a weight function . We define the {\em weighted extremal number} \[ \mathrm{ex}(n,w,F):=\max\{w(G)\mid G\subseteq K_n,\text{ a…
The bipartite -free process and bipartite Ramsey number
Deepak Bal, Patrick Bennett
The bipartite Ramsey number is the smallest integer such that every blue-red edge coloring of contains either a blue or a red . In the bip…
Minimizing the number of 5-cycles in graphs with given edge-density
Patrick Bennett, Andrzej Dudek, Bernard Lidický +1
Motivated by the work of Razborov about the minimal density of triangles in graphs we study the minimal density of the 5-cycle . We show that every graph of order and size…