Department of
Applied
Mathematics

On the directed cycle double cover Conjecture

Andrea Jiménez

Abstract

In this talk, we discuss our recent progress on the famous Jaeger's directed cycle double cover conjecture from graph theory. This conjecture asserts that every 2-connected graph admits a collection of cycles such that each edge is in exactly two cycles of the collection. In addition, it must be possible to prescribe an orientation to each cycle so that each edge is traversed in both ways.

So far, we have developed two theories around Jaeger's conjecture. In this talk, we intend to present them. Both theories concern a wide variety of topics, such as embeddings of graphs, matching theory, generation of graphs and connectivity theory.

This is a joint work with Mihyun Kang and Martin Loebl.