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Jaeger, Francois
Mapping planar graphs to odd cycles ★★★
Author(s): Jaeger
Conjecture Every planar graph of girth
has a homomorphism to
.
![$ \ge 4k $](/files/tex/cf3c6265929d41a26d0297d4ba26c602e0e2d93b.png)
![$ C_{2k+1} $](/files/tex/f20c34c1abcdfc50a63f8c5920f0ddb51a9f7cae.png)
Keywords: girth; homomorphism; planar graph
The additive basis conjecture ★★★
Author(s): Jaeger; Linial; Payan; Tarsi
Conjecture For every prime
, there is a constant
(possibly
) so that the union (as multisets) of any
bases of the vector space
contains an additive basis.
![$ p $](/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png)
![$ c(p) $](/files/tex/996da72e7b0b6591ec8cc40dcbe46964d764e211.png)
![$ c(p)=p $](/files/tex/b1a6c0fbe5cae8582d2ef00c5f0f5158c9d9d4be.png)
![$ c(p) $](/files/tex/996da72e7b0b6591ec8cc40dcbe46964d764e211.png)
![$ ({\mathbb Z}_p)^n $](/files/tex/ea205f9e138abfc9a2c6a35332ecc6694ebe6419.png)
Keywords: additive basis; matrix
A nowhere-zero point in a linear mapping ★★★
Author(s): Jaeger
Conjecture If
is a finite field with at least 4 elements and
is an invertible
matrix with entries in
, then there are column vectors
which have no coordinates equal to zero such that
.
![$ {\mathbb F} $](/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png)
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ n \times n $](/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png)
![$ {\mathbb F} $](/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png)
![$ x,y \in {\mathbb F}^n $](/files/tex/817584f802a24b69508ae913bf47b34d6ff78ca8.png)
![$ Ax=y $](/files/tex/6fc49872cdb030ca09b427d20b9fd3b1d3873641.png)
Keywords: invertible; nowhere-zero flow
Jaeger's modular orientation conjecture ★★★
Author(s): Jaeger
Keywords: nowhere-zero flow; orientation
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