2013/01/28 by Andrew Steane, Andrew M. Steane, Steane, Andrew M.
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Game Theory and Applications #math.CO
paper · pdf · doi:10.48550/arxiv.1301.6612
25 pages, 8 main figures plus various further diagrams
arxiv created 2013/01/28 · openalex publication_date 2013/01/28 · arxiv updated 2013/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.