6 papers
Counting Hamiltonian Cycles in Dirac Hypergraphs
Asaf Ferber, Liam Hardiman, Adva Mond
For , a Hamiltonian -cycle in a -uniform hypergraph is a cyclic ordering of the vertices of in which the edges are segments of length and every…
The Maker-Breaker percolation game on the square lattice
Vojtěch Dvořák, Adva Mond, Victor Souza
We study the Maker-Breaker percolation game on , introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the…
Turán-type problems for long cycles in random and pseudo-random graphs
Michael Krivelevich, Gal Kronenberg, Adva Mond
We study the Turán number of long cycles in random graphs and in pseudo-random graphs. Denote by the random variable counting the number of edges in a largest subgra…
On the Odd Cycle Game and Connected Rules
Jan Corsten, Adva Mond, Alexey Pokrovskiy +2
We study the positional game where two players, Maker and Breaker, alternately select respectively and previously unclaimed edges of . Maker wins if she succeeds in cl…
-games played on vertex sets of random graphs
Gal Kronenberg, Adva Mond, Alon Naor
We introduce a new type of positional games, played on a vertex set of a graph. Given a graph , two players claim vertices of , where the outcome of the game is determined by…
The Minrank of Random Graphs over Arbitrary Fields
Noga Alon, Igor Balla, Lior Gishboliner +2
The minrank of a graph on the set of vertices over a field is the minimum possible rank of a matrix with nonzero diagonal entrie…