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JCT
2000
14 years 9 months ago
2000
We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm does not use the ellipsoid method or any other linear ...
JCT
2002
14 years 9 months ago
2002
We prove that 45 is the size of the largest caps in AG(5, 3), and such a 45-cap is always obtained from the 56-cap in PG(5, 3) by deleting an 11-hyperplane.
JCT
1998
14 years 9 months ago
1998
If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs ...
JCT
2010
14 years 8 months ago
2010
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by prec...
JCT
2010
14 years 8 months ago
2010
We prove that every graph with maximum degree ∆ can be properly (∆ + 1)coloured so that no colour appears more than O(log ∆/ log log ∆) times in the neighbourhood of any v...