Subgraphs of colour-critical graphs (Q1101121)

The author shows that if \(k\geq 4\) is an integer, then there exists a positive integer \(n_ 0=n_ 0(k)\) such that the folloollipop graphs'' used by Thomason. G(\(\Delta)\) is defined as follows: If G is a graph with vertex set V(G) and \(\Delta\) a set of triangles of G, G(\(\Delta)\) is that bipartite graph on V(G)\(\cup \Delta\) such that \(v\in V(G)\) is adjacent to a triangle \(\delta\in \Delta\) if \(v\in \delta\).