Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal and irreducible links in the Shannon game   We discuss weak and strong links (`virtual connections') in the Shannon game.
General properties of these links are discussed, leading to a method to find
all links of given size by a suitably pruned exhaustive search. This is applied
to links on graphs of up to 11 vertices. We discuss the concept of reducibility
of such links. Three simple reductions are considered, including one, the
`short-cut', not previously described. The complete sets of irreducible weak
links on up to 11 vertices and strong links on up to 10 vertices are presented.
Some applications to the analysis of Hex are noted.

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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin