More counterexamples to the Alon-Saks-Seymour and rank-coloring conjectures
The Rank-Coloring Conjecture states that the chromatic number \(\chi(G) \leq rank(A(G))\), the rank of the adjacency matrix of the graph \(G\). The Alon, Saks, and Seymour Conjecture states that \(\chi(G) \leq bp(G) + 1\), where \(bp(G)\) is the complete bipartite partition number for the graph \(G\). Using a family of graphs \(G(n, k, r)\), which are patterned after \(n\)-dimensional cube \(Q_n\), they give counterexamples to each of the previously mentioned Conjectures.
scientific article; zbMATH DE number 5852476
scientific article