***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000741 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The Colin de Verdière graph invariant. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Colin_de_Verdière_graph_invariant]] [2] van der Holst, H., Lovász, L., Schrijver, A. The Colin de Verdière graph parameter [[MathSciNet:1673503]] [3] Goldberg, F., Berman, A. On the Colin de Verdière number of graphs [[MathSciNet:2775745]] [4] Tait, M. The Colin de Verdi\`ere parameter, excluded minors, and the spectral radius [[arXiv:1703.09732]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ([],1) => 0 ([],2) => 1 ([(0,1)],2) => 1 ([],3) => 1 ([(0,2),(1,2)],3) => 2 ([(0,1),(0,2),(1,2)],3) => 2 ([],4) => 1 ([(1,3),(2,3)],4) => 1 ([(0,3),(1,3),(2,3)],4) => 2 ([(0,3),(1,2),(2,3)],4) => 1 ([(1,2),(1,3),(2,3)],4) => 2 ([(0,3),(1,2),(1,3),(2,3)],4) => 2 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3 ([],5) => 1 ([(2,4),(3,4)],5) => 1 ([(0,4),(1,4),(2,4),(3,4)],5) => 2 ([(1,4),(2,3),(3,4)],5) => 1 ([(0,1),(2,4),(3,4)],5) => 1 ([(2,3),(2,4),(3,4)],5) => 2 ([(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,3),(2,3),(2,4)],5) => 1 ([(0,1),(2,3),(2,4),(3,4)],5) => 2 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 2 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4 ([],6) => 1 ([(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2 ([(2,5),(3,4),(4,5)],6) => 1 ([(1,2),(3,5),(4,5)],6) => 1 ([(3,4),(3,5),(4,5)],6) => 2 ([(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,4),(3,4)],6) => 1 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(1,5),(2,4),(3,4),(3,5)],6) => 1 ([(0,1),(2,5),(3,4),(4,5)],6) => 1 ([(1,2),(3,4),(3,5),(4,5)],6) => 2 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 2 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 2 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ----------------------------------------------------------------------------- Created: Mar 30, 2017 at 09:11 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 31, 2017 at 11:31 by Martin Rubey