# Bojan Mohar: Paths and trails of odd length and totally odd immersions of graphs

Date: 22. 5. 2017

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 23. 5. 2017, od 10h do 12h, Plemljev seminar, Jadranska 19

**Povzetek.**One of the milestones in graph theory is Menger's Theorem which states that the maximum number of edge-disjoint paths between two vertices

*u*and

*v*is equal to the minimum number of edges whose removal disconnects

*u*from

*v*. If we want paths from

*u*to

*v*having additional properties, for example being of odd length, this exact duality no longer holds. However, a kind of weak duality can be achieved. This problem and its resolution will be discussed and some of its applications will be presented. In particular, totally odd immersions of graphs are tightly related to this topic.