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» A note on the Gallai-Roy-Vitaver Theorem
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DCG
2010
146views more  DCG 2010»
13 years 5 months ago
An Elementary Deduction of the Topological Radon Theorem from Borsuk-Ulam
Abstract. The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn , there exist a pair of disjoint faces...
Craig R. Guilbault
CORR
2010
Springer
60views Education» more  CORR 2010»
13 years 8 months ago
A Note on Integer Factorization Using Lattices
We revisit Schnorr's lattice-based integer factorization algorithm, now with an effective point of view. We present effective versions of Theorem 2 of [11], as well as new pro...
Antonio Ignacio Vera
DM
2006
54views more  DM 2006»
13 years 8 months ago
A note on interconnecting matchings in graphs
We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph of G. The condition is derived from a re...
Tomás Kaiser
AML
2011
204views Mathematics» more  AML 2011»
13 years 2 months ago
A note on propositional proof complexity of some Ramsey-type statements
Any valid Ramsey statement n −→ (k)2 2 can be encoded into a DNF formula RAM(n, k) of size O(nk) and with terms of size k 2 . Let rk be the minimal n for which the statement h...
Jan Krajícek
CORR
2010
Springer
109views Education» more  CORR 2010»
13 years 8 months ago
Optimal Direct Sum Results for Deterministic and Randomized Decision Tree Complexity
A Direct Sum Theorem holds in a model of computation, when for every problem solving some k input instances together is k times as expensive as solving one. We show that Direct Su...
Rahul Jain, Hartmut Klauck, Miklos Santha