Graph Theory » Directed Graphs

The Bermond-Thomassen Conjecture ★★

Author(s): Bermond; Thomassen

Conjecture   For every positive integer $ k $, every digraph with minimum out-degree at least $ 2k-1 $ contains $ k $ disjoint cycles.

Keywords: cycles

Posted by JS
updated October 1st, 2007
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Geometry » Polytopes

Continous analogue of Hirsch conjecture ★★

Author(s): Deza; Terlaky; Zinchenko

Conjecture   The order of the largest total curvature of the primal central path over all polytopes defined by $ n $ inequalities in dimension $ d $ is $ n $.

Keywords: curvature; polytope

Posted by deza
updated September 30th, 2007
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Geometry

Average diameter of a bounded cell of a simple arrangement ★★

Author(s): Deza; Terlaky; Zinchenko

Conjecture   The average diameter of a bounded cell of a simple arrangement defined by $ n $ hyperplanes in dimension $ d $ is not greater than $ d $.

Keywords: arrangement; diameter; polytope

Posted by deza
updated September 30th, 2007
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