![](/files/happy5.png)
tension
5-local-tensions ★★
Author(s): DeVos
Conjecture There exists a fixed constant
(probably
suffices) so that every embedded (loopless) graph with edge-width
has a 5-local-tension.
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ c=4 $](/files/tex/b1faa9584556785b57e447d15d1d2178572c5d90.png)
![$ \ge c $](/files/tex/4955fa317e705797fabe67a986cb7273813cce12.png)
A homomorphism problem for flows ★★
Author(s): DeVos
Conjecture Let
be abelian groups and let
and
satisfy
and
. If there is a homomorphism from
to
, then every graph with a B-flow has a B'-flow.
![$ M,M' $](/files/tex/4bd0590f5618f9306e6f1a2fe10e8b811859c1d9.png)
![$ B \subseteq M $](/files/tex/0841b3f2c65d1f2fa19ef611b62df2cbe21b707b.png)
![$ B' \subseteq M' $](/files/tex/3be253a61ac2430d053b2c331b9d0516305f8116.png)
![$ B=-B $](/files/tex/44dba92dfcc7e25e513f45325ee83a69a896eb1c.png)
![$ B' = -B' $](/files/tex/8fce1069de40506650f70aa0d0ee79f5a36ed456.png)
![$ Cayley(M,B) $](/files/tex/5264bebd8d0c334fec1533103d0f600b665604c2.png)
![$ Cayley(M',B') $](/files/tex/e2d1e39749b1550537591fb4ea1057b69feb5bb0.png)
Keywords: homomorphism; nowhere-zero flow; tension
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