481 research outputs found
An interpolation theorem for proper holomorphic embeddings
Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and
a discrete sequence b_j in C^m where m > [3n/2], there exists a proper
holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,....
This is the interpolation version of the embedding theorem due to Eliashberg,
Gromov and Schurmann. The dimension m cannot be lowered in general due to an
example of Forster
A note on "Folding wheels and fans."
In S.Gervacio, R.Guerrero and H.Rara, Folding wheels and fans, Graphs and
Combinatorics 18 (2002) 731-737, the authors obtain formulas for the clique
numbers onto which wheels and fans fold. We present an interpolation theorem
which generalizes their theorems 4.2 and 5.2. We show that their formula for
wheels is wrong. We show that for threshold graphs, the achromatic number and
folding number coincides with the chromatic number
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