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JCT
2006
14 years 9 months ago
2006
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....
JCT
2006
14 years 9 months ago
2006
The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension n. Given any ellipsoid, our goal is to find the minimum number of unit balls nee...
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JCT
2006
14 years 9 months ago
2006
Nash-Williams' arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of vertices induces more than k( - 1) edges. We prove a...
JCT
2006
14 years 9 months ago
2006
The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J....
JCT
2006
14 years 9 months ago
2006
We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded ...