# Jaeger, Francois

## Mapping planar graphs to odd cycles ★★★

Author(s): Jaeger

**Conjecture**Every planar graph of girth has a homomorphism to .

Keywords: girth; homomorphism; planar graph

## The additive basis conjecture ★★★

Author(s): Jaeger; Linial; Payan; Tarsi

**Conjecture**For every prime , there is a constant (possibly ) so that the union (as multisets) of any bases of the vector space contains an additive basis.

Keywords: additive basis; matrix

## A nowhere-zero point in a linear mapping ★★★

Author(s): Jaeger

**Conjecture**If is a finite field with at least 4 elements and is an invertible matrix with entries in , then there are column vectors which have no coordinates equal to zero such that .

Keywords: invertible; nowhere-zero flow

## Jaeger's modular orientation conjecture ★★★

Author(s): Jaeger

**Conjecture**Every -edge-connected graph can be oriented so that (mod ) for every vertex .

Keywords: nowhere-zero flow; orientation