... where A(G) is the adjacency matrix of G. Thenχ(G)=3 2and the electronic journal of combinatorics 4 (1997), #R19 3 and α(G) < min{ rank(B) |B ∈B(G)}by theorem.Acknowledgement. The author is ... Gr¨otschel, L´aszl´oLov´asz, and Alexander Schrijver, Geometric Algorithms and Combina-torial Optimization (Springer-Verlag, 1988).3. Donald E.Knuth, The Sandwich Theorem”, Electronic J. Combinatorics ... rank(B)=α(G).Equation (1) gives us further information about the graph G.(i) If v ∈S then exists u ∈ S such that u −− v. Indeed, Yvv= 1 and Xwv≥ 0 for all w ∈ S.Hence,w∈SX2wv= 1 and Xuv> 0 for...