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6 papers · 2 filters
A quadratic lower bound for colourful simplicial depth
Tamon Stephen, Hugh Thomas
We show that any point in the convex hull of each of (d+1) sets of (d+1) points in R^d is contained in at least floor((d+2)^2/4) simplices with one vertex from each set.
Colorful subgraphs in Kneser-like graphs
Gábor Simonyi, Gábor Tardos
Combining Ky Fan's theorem with ideas of Greene and Matousek we prove a generalization of Dol'nikov's theorem. Using another variant of the Borsuk-Ulam theorem due to Bacon and Tuc…
The Colourful Feasibility Problem
Antoine Deza, Sui Huang, Tamon Stephen +1
We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking o…
Automatic enumeration of regular objects
Marni Mishna
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differenti…
Colourful Simplicial Depth
Antoine Deza, Sui Huang, Tamon Stephen +1
Inspired by Barany's colourful Caratheodory theorem, we introduce a colourful generalization of Liu's simplicial depth. We prove a parity property and conjecture that the minimum c…
Local chromatic number and distinguishing the strength of topological obstructions
Gábor Simonyi, Gábor Tardos, Siniša T. Vrećica
The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G. We show tha…