DescriptionPlane substructures in drawings of graphs are an active area of research. Among other things, they may be useful to prove structural or combinatorial results on the underlying graphs. For example, a lower bound on the number of combinatorially different simple drawings of the complete graph has been shown under the assumption that each such drawing contains a plane Hamiltonian cycle. However, it is still open whether this assumption holds as finding plane substructures in those drawings turns out to be surprisingly difficult.
In my talk, I discuss recent improvements on lower bounds for the number of pairwise disjoint edges and the length of plane paths in simple drawings of complete graphs. A main ingredient is a special class of simple drawings that we call generalized twisted drawings. These have surprising properties and might also be of interest for other questions.
|Period||3 Jun 2022|
|Event title||AMSI–AustMS Workshop on Bridging Maths and Computer Science|
|Location||Sydney, AustraliaShow on map|
|Degree of Recognition||International|