Subgraphs of colour-critical graphs

Some problems and results on the distribution of subgraphs in colour-critical graphs are discussed.In section 3 arbitrarily largek-critical graphs withn vertices are constructed such that, in order to reduce the chromatic number tok−2, at leastckn2 edges must be removed.In section 4 it is proved that a 4-critical graph withn vertices contains at mostn triangles. Further it is proved that ak-critical graph which is not a complete graph contains a (k−1)-critical graph which is not a complete graph.