ACTA
2000
13 years 11 months ago
2000
The paper refers to the Collatz's conjecture. In the first part, we present some equivalent forms of this conjecture and a slight generalization of a former result from [1]. T...
CAGD
2004
13 years 11 months ago
2004
This note conjectures that if two surface patches intersect with G1 continuity along an entire curve, the probability is one that the curve is rational. This idea has significance...
JCT
2007
13 years 11 months ago
2007
Kreweras’ conjecture [1] asserts that any perfect matching of the hypercube Qd, d ≥ 2, can be extended to a Hamilton cycle. We prove this conjecture.
JCT
2007
13 years 11 months ago
2007
We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z2k+1 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two co...
SIAMDM
2008
13 years 11 months ago
2008
In [5], Reed conjectures that every graph satisfies ++1 2 . We prove this holds for graphs with disconnected complement. Combining this fact with a result of Molloy proves the co...
SIAMDM
2008
13 years 11 months ago
2008
We prove a conjecture of Erdos, Purdy, and Straus on the number of distinct areas of triangles determined by a set of n points in the plane. We show that if P is a set of n points...
ORL
2008
13 years 11 months ago
2008
By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities de...
ORL
2008
13 years 11 months ago
2008
The VPN Tree Routing Conjecture states that there always exists an optimal solution to the symmetric Virtual Private Network Design (sVPND) problem where the paths between all ter...
ENDM
2007
13 years 11 months ago
2007
Kreweras’ conjecture [9] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle of Qd. We [5] proved this conjecture but here we present ...
ECCC
2007
13 years 11 months ago
2007
Abstract: We give an explicit construction of a pseudorandom generator against lowdegree polynomials over finite fields. Pseudorandom generators against linear polynomials, known...