![](/files/happy5.png)
Nowhere-zero flows
Open problems about Nowhere-zero flows (not to be confused with Network flows).
5-flow conjecture ★★★★
Author(s): Tutte
Keywords: cubic; nowhere-zero flow
3-flow conjecture ★★★
Author(s): Tutte
Keywords: nowhere-zero flow
Jaeger's modular orientation conjecture ★★★
Author(s): Jaeger
Keywords: nowhere-zero flow; orientation
Bouchet's 6-flow conjecture ★★★
Author(s): Bouchet
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ 6 $](/files/tex/b1111b1328c0de162c7bb7bdbde0496f3f37f563.png)
Keywords: bidirected graph; nowhere-zero flow
The three 4-flows conjecture ★★
Author(s): DeVos
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ A_1,A_2,A_3 \subseteq E(G) $](/files/tex/00b3c9754dad6733bd2accc303abd67548500b18.png)
![$ A_1 \cup A_2 \cup A_3 = E(G) $](/files/tex/9221eff05fcc813555f4a22eb3ce690354664239.png)
![$ G \setminus A_i $](/files/tex/880e1ceffd87347d797ae0d4e59d524734f42f73.png)
![$ 1 \le i \le 3 $](/files/tex/f40f4d8f17c01da8627f69cc31a03ec8efa58853.png)
Keywords: nowhere-zero flow
A homomorphism problem for flows ★★
Author(s): DeVos
![$ 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') $](/files/tex/e2d1e39749b1550537591fb4ea1057b69feb5bb0.png)
Keywords: homomorphism; nowhere-zero flow; tension
Real roots of the flow polynomial ★★
Author(s): Welsh
Keywords: flow polynomial; nowhere-zero flow
Unit vector flows ★★
Author(s): Jain
![$ q:S^2 \rightarrow \{-4,-3,-2,-1,1,2,3,4\} $](/files/tex/9e1061f676e5ae08c4736731352fdc62d6f50c6c.png)
![$ S^2 $](/files/tex/1cd459995f11529f346339e6879cf139c22ee92c.png)
Keywords: nowhere-zero flow
Antichains in the cycle continuous order ★★
Author(s): DeVos
If ,
are graphs, a function
is called cycle-continuous if the pre-image of every element of the (binary) cycle space of
is a member of the cycle space of
.
![$ \{G_1,G_2,\ldots \} $](/files/tex/8c2ee68229cfd0ed4b4be107c721fb5ab4204c18.png)
![$ G_i $](/files/tex/49c5f06ff437d0aa89130ae9b5fba029a520a65a.png)
![$ G_j $](/files/tex/a26853e93bc552976a6a2d1f0b66796c063820ae.png)
![$ i \neq j $](/files/tex/5c06b842f91344e3271e846fd6bff4dc9fb4ab0d.png)
Circular flow number of regular class 1 graphs ★★
Author(s): Steffen
A nowhere-zero -flow
on
is an orientation
of
together with a function
from the edge set of
into the real numbers such that
, for all
, and
. The circular flow number of
is inf
has a nowhere-zero
-flow
, and it is denoted by
.
A graph with maximum vertex degree is a class 1 graph if its edge chromatic number is
.
![$ t \geq 1 $](/files/tex/f9082ade09146d7aa9994735ba4ad788d0583b0c.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ (2t+1) $](/files/tex/da4d60d92c98256f762bb69398437f3914ef0fa6.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ F_c(G) \leq 2 + \frac{2}{t} $](/files/tex/35f6f6ba01e2a1f8f2c867888c086731d735cc74.png)
![Syndicate content Syndicate content](/misc/feed.png)