80 research outputs found
Improved Delsarte bounds for spherical codes in small dimensions
We present an extension of the Delsarte linear programming method. For
several dimensions it yields improved upper bounds for kissing numbers and for
spherical codes. Musin's recent work on kissing numbers in dimensions three and
four can be viewed in our framework.Comment: 16 pages, 3 figures. Substantial changes after referee's comments,
one new lemm
Total weight choosability in Hypergraphs
A total weighting of the vertices and edges of a hypergraph is called
vertex-coloring if the total weights of the vertices yield a proper coloring of
the graph, i.e., every edge contains at least two vertices with different
weighted degrees. In this note we show that such a weighting is possible if
every vertex has two, and every edge has three weights to choose from,
extending a recent result on graphs to hypergraphs
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