Snarks and their generalizations: r-graphs

• Applicant: Professor Dr. Eckhard Steffen
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 546530571

Many important questions in graph theory (such as the 5-flow conjecture or the cycle double cover conjecture) can be reduced to the class of cubic graphs. In fact, it suffices to solve them for bridgeless cubic graphs that do not admit a 3-edge coloring, the so-called snarks. Due to their importance, the study of snarks is a very active area of research in graph theory. Many of the problems reducible to snarks have natural generalizations for r-regular graphs with r>3, so that in recent years this class of graphs has become an increasing focus of mathematical research. In the project, these graphs are studied in order to gain new insights into the interaction of methods and properties between the r=3 case and the general case. This is done with reference to the finer classification of r-regular graphs (r>3) with respect to pairwise disjoint perfect matchings, which does not exist for cubic graphs.

• DFG Programme: Research Grants