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COMBINATORICA
2011
8 years 2 months ago
Binary subtrees with few labeled paths
We prove several quantitative Ramseyan results involving ternary complete trees with {0, 1}-labeled edges where we attempt to find a complete binary subtree with as few labels as ...
Rodney G. Downey, Noam Greenberg, Carl G. Jockusch...
COMBINATORICA
2011
8 years 2 months ago
A q-analogue of the FKG inequality and some applications
Let L be a finite distributive lattice and µ : L → R+ a logsupermodular function. For functions k : L → R+ let Eµ(k; q) def = x∈L k(x)µ(x)qrank(x) ∈ R+ [q]. We prove fo...
Anders Björner
COMBINATORICA
2011
8 years 2 months ago
A local criterion for Tverberg graphs
The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)-simplex to Rd , there are q disjoint faces Fi of the simplex whose im...
Alexander Engström
COMBINATORICA
2011
8 years 2 months ago
On planarity of compact, locally connected, metric spaces
Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2–connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it doe...
R. Bruce Richter, Brendan Rooney, Carsten Thomasse...
COMBINATORICA
2011
8 years 2 months ago
On the chromatic number of random geometric graphs
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
Colin McDiarmid, Tobias Müller
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