## Combinatorics Seminar - Spring '21

When: Sunday, May 9, 10am

Where: Schreiber 309

Speaker: Gal Kronenberg,
Oxford University

Title:
Partitioning Cubic Graphs into Isomorphic Linear Forests

## Abstract:

The linear arboricity of a graph $G$, denoted by la($G$), is the minimum
number of edge-disjoint linear forests (i.e. collections of disjoint
paths) in $G$ whose union is all the edges of $G$. It is known that the
linear
arboricity of every cubic graph is 2. In 1987 Wormald conjectured that
every cubic graph with even number of edges, can be partitioned such that
the two parts are isomorphic linear forests.
This is known to hold for Jeager graphs and for some further classes of
cubic graphs (see, Bermond-Fouquet-Habib-Peroche, Wormald,
Jackson-Wormald, Fouquet-Thuillier-Vanherpe-Wojda).
In this talk we will present a proof of Wormald's conjecture for all large
connected cubic graphs.

This is joint work with Shoham Letzter, Alexey Pokrovskiy, and Liana
Yepremyan.