The stable-set bound for simple 4-polytopes with 9 facets: This file documents data for the article: Constantin Ickstadt, Thorsten Theobald and Bernhard von Stengel: A Stable-Set Bound and Maximal Numbers of Nash Equilibria in Bimatrix Games, arXiv:2411.12385 Link to accompanying Web page: https://www.math.uni-frankfurt.de/~ickstadt/nash-5x5/ ---------------------------------------------------------------------- For each of the 1142 simple 4-polytopes with 9 facets, the following table shows: In column "No.": an ordering number from 1 to 1297, the order of the polytopes comes from the order in the data of Firsching's classification [1]. That classification uses the language of simplicial polytopes, which is dual to our setting. In column 2: the number of vertices of the simple 5-polytope with 9 facets In column 3: twice the size of a largest stable set in the graph (which is an upper bound on the stable-set bound) In column 4: the stable-set bound In column 5: the number of 3-dimensional facets which are 3-cubes Reference: [1] M. Firsching: https://ftp.imp.fu-berlin.de/pub/moritz/inscribe/neighborly/ also available on firsching.ch No. 2 3 4 5 ---------------------------------- 1 19 16 16 4 2 21 16 16 2 3 20 16 16 3 4 19 12 12 0 5 18 12 12 0 6 19 12 12 0 7 20 14 14 0 8 23 16 16 0 9 21 14 14 0 10 22 16 16 0 11 20 16 16 5 12 19 14 14 1 13 20 14 14 0 14 22 16 16 0 15 20 14 14 0 16 20 16 16 2 17 21 16 16 1 18 21 16 16 0 19 19 14 12 0 20 18 12 12 0 21 22 16 16 1 22 17 10 10 0 23 18 12 12 0 24 18 12 12 0 25 19 14 12 1 26 19 14 12 0 27 19 14 14 0 28 19 14 12 0 29 20 14 14 1 30 20 14 14 0 31 21 16 14 0 32 21 16 16 1 33 20 14 14 0 34 21 16 14 0 35 20 14 12 0 36 21 14 14 0 37 20 14 14 0 38 21 16 14 0 39 21 16 14 0 40 22 16 16 0 41 22 16 16 0 42 22 16 16 0 43 23 16 16 0 44 22 16 16 0 45 22 16 16 0 46 22 16 16 0 47 21 16 16 0 48 22 16 16 0 49 21 16 14 0 50 21 16 14 0 51 20 14 14 0 52 21 16 16 0 53 20 14 14 0 54 21 16 16 1 55 22 16 16 0 56 22 18 16 1 57 22 18 16 1 58 25 20 20 0 59 24 18 18 0 60 23 18 18 1 61 24 20 18 1 62 23 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