11 papers
Oriented cycles in digraphs of large outdegree
Lior Gishboliner, Raphael Steiner, Tibor Szabó
In 1985, Mader conjectured that for every acyclic digraph there exists such that every digraph with minimum out-degree at least contains a subdivision of .…
Dichromatic number and forced subdivisions
Lior Gishboliner, Raphael Steiner, Tibor Szabó
We investigate bounds on the dichromatic number of digraphs which avoid a fixed digraph as a topological minor. For a digraph , denote by the smallest…
Ryser's Conjecture for -intersecting hypergraphs
Anurag Bishnoi, Shagnik Das, Patrick Morris +1
A well-known conjecture, often attributed to Ryser, states that the cover number of an -partite -uniform hypergraph is at most times larger than its matching number.…
Majority Colorings of Sparse Digraphs
Michael Anastos, Ander Lamaison, Raphael Steiner +1
A majority coloring of a directed graph is a vertex-coloring in which every vertex has the same color as at most half of its out-neighbors. Kreutzer, Oum, Seymour, van der Zypen an…
Enumerating extensions of mutually orthogonal Latin squares
Simona Boyadzhiyska, Shagnik Das, Tibor Szabó
Two Latin squares are said to be orthogonal if, for every ordered pair of symbols, there are coordinates such that and $L_2(i…
Singer difference sets and the projective norm graph
Tamás Mészáros, Lajos Rónyai, Tibor Szabó
We demonstrate a close connection between the classic planar Singer difference sets and certain norm equation systems arising from projective norm graphs. This, on the one hand lea…