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LICS
1999
IEEE
13 years 9 months ago
First-Order Logic vs. Fixed-Point Logic in Finite Set Theory
The ordered conjecture states that least fixed-point logic LFP is strictly more expressive than first-order logic FO on every infinite class of ordered finite structures. It has b...
Albert Atserias, Phokion G. Kolaitis
JSC
2008
58views more  JSC 2008»
13 years 5 months ago
A Groebner basis approach to solve a Conjecture of Nowicki
Let k be a field of characteristic zero, n any positive integer and let n be the derivation n i=1 Xi Yi of the polynomial ring k[X1, . . . , Xn, Y1, . . . , Yn] in 2n variables o...
Joseph Khoury
STOC
1996
ACM
100views Algorithms» more  STOC 1996»
13 years 9 months ago
The Linear-Array Conjecture in Communication Complexity is False
A linear array network consists of k + 1 processors P0; P1; : : : ; Pk with links only between Pi and Pi+1 0 i k. It is required to compute some boolean function f x; y in this n...
Eyal Kushilevitz, Nathan Linial, Rafail Ostrovsky
JGT
2010
152views more  JGT 2010»
13 years 10 days ago
Cycles of even lengths modulo k
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
Ajit A. Diwan
COMBINATORICS
2006
121views more  COMBINATORICS 2006»
13 years 5 months ago
Edge and Total Choosability of Near-Outerplanar Graphs
It is proved that, if G is a K4-minor-free graph with maximum degree 4, then G is totally ( + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ...
Timothy J. Hetherington, Douglas R. Woodall