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18 papers · 1 filter
A family of reductions for Schubert intersection problems
H. Bercovici, W. S. Li, D. Timotin
We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions…
The Discrepancy of the Lex-Least De Bruijn Sequence
Joshua Cooper, Christine Heitsch
We answer the following question of R. L. Graham: What is the discrepancy of the lexicographically-least binary de Bruijn sequence? Here, "discrepancy" refers to the maximum (absol…
On the Density of a Graph and its Blowup
Asaf Shapira, Raphael Yuster
The theorem of Chung, Graham, and Wilson on quasi-random graphs asserts that of all graphs with edge density p, the random graph G(n,p) contains the smallest density of copies of K…
Multigraphs (only) satisfy a weak triangle removal lemma
Asaf Shapira, Raphael Yuster
The triangle removal lemma states that a simple graph with o(n^3) triangles can be made triangle-free by removing o(n^2) edges. It is natural to ask if this widely used result can…
Intersection Graphs of Pseudosegments: Chordal Graphs
Cornelia Dangelmayr, Stefan Felsner, William T. Trotter
We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. For positive we have a construction which shows that all chordal graphs that can…
On rich lines in grids
Evan Borenstein, Ernie Croot
In this paper we show that if one has a grid A x B, where A and B are sets of n real numbers, then there can be only very few ``rich'' lines in certain quite small families. Indeed…