PUB - Publikationen an der Universität Bielefeld

We consider graphs and multigraphs which are critical with respect to the chromatic index. In chapter 3, we give a construction of critical multigraphs with exactly 20 vertices and maximum degree k for every k>=5. This disproves the weak critical graph conjecture. In chapter 4, we give a new method, how several 4-critical multigraphs can be constructed from a given 3-critical graph. In chapter 5, we prove that the edges of every planar graph with maximum degree 7 can be colored with 7 colors. This proves one of the two open cases of Vizing's planar graph conjecture from 1965.