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Jaeger, Francois


Graph Theory » Coloring » Homomorphisms

Mapping planar graphs to odd cycles ★★★

Author(s): Jaeger

Conjecture   Every planar graph of girth $ \ge 4k $ has a homomorphism to $ C_{2k+1} $.

Keywords: girth; homomorphism; planar graph

Posted by mdevos
updated June 24th, 2007
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Combinatorics » Matrices

The additive basis conjecture ★★★

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

Conjecture   For every prime $ p $, there is a constant $ c(p) $ (possibly $ c(p)=p $) so that the union (as multisets) of any $ c(p) $ bases of the vector space $ ({\mathbb Z}_p)^n $ contains an additive basis.

Keywords: additive basis; matrix

Posted by mdevos
updated March 8th, 2007
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Combinatorics » Matrices

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

Author(s): Jaeger

Conjecture   If $ {\mathbb F} $ is a finite field with at least 4 elements and $ A $ is an invertible $ n \times n $ matrix with entries in $ {\mathbb F} $, then there are column vectors $ x,y \in {\mathbb F}^n $ which have no coordinates equal to zero such that $ Ax=y $.

Keywords: invertible; nowhere-zero flow

Posted by mdevos
updated March 8th, 2007
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Graph Theory » Coloring » Edge coloring

Petersen coloring conjecture ★★★

Author(s): Jaeger

Conjecture   Let $ G $ be a cubic graph with no bridge. Then there is a coloring of the edges of $ G $ using the edges of the Petersen graph so that any three mutually adjacent edges of $ G $ map to three mutually adjancent edges in the Petersen graph.

Keywords: cubic; edge-coloring; Petersen graph

Posted by mdevos
updated November 24th, 2011
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Graph Theory » Coloring » Nowhere-zero flows

Jaeger's modular orientation conjecture ★★★

Author(s): Jaeger

Conjecture   Every $ 4k $-edge-connected graph can be oriented so that $ {\mathit indegree}(v) - {\mathit outdegree}(v) \cong 0 $ (mod $ 2k+1 $) for every vertex $ v $.

Keywords: nowhere-zero flow; orientation

Posted by mdevos
updated March 7th, 2007
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