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JCT
2000
14 years 11 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 11 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 11 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 10 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...
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JCT
2010
14 years 10 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...