U-STARUndergraduate Student Training in Academic Research
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In the final, the winner will be named Vietnam's U-STAR and will receive a valuable award.
U-STAR will officially launch in Vietnam in Jan 2017.
, [G.sub.t]} of consecutively ordered U-stars will be referred to as a consecutive U-star partition (CUSP) of G.
Theorem 1.2 (Brown, Lundgren, [6]) A bipartite graph G is a probe interval graph if and only if it has a consecutive U-star partition.
If G = (X, Y, E) is convex with, say, Nx consecutively ordered, then we can take Y = U and X = N and the collection {{y} U N(y) : y [member of] Y} is a consecutively orderable U-star partition.
Also, H10 has no consecutive U-star partition, but the structure it has which we generalize and use for the recognition algorithm is as follows.
Furthermore, from the definition of a U-star, and using [c.sub.r] to denote the center of [U.sub.r], it follows that [c.sub.i] [member of] Y, [c.sub.j] [member of] X, and that for each k satisfying i < k < j, [U.sub.k] is a cut-edge of H.
Finally, we show that the U-stars of any CUSP for any [??] corresponding to bipartite probe interval graph G must be chosen so that the vertices [??], w" of a 3-path incident to w [member of] [partial derivative]H are in the first or last U-star of the CUSP.