
Arthur
3-Edge-Coloring Conjecture ★★★
Author(s): Arthur; Hoffmann-Ostenhof
Conjecture Suppose
with
is a connected cubic graph admitting a
-edge coloring. Then there is an edge
such that the cubic graph homeomorphic to
has a
-edge coloring.






Keywords: 3-edge coloring; 4-flow; removable edge
Cycle Double Covers Containing Predefined 2-Regular Subgraphs ★★★
Author(s): Arthur; Hoffmann-Ostenhof
Conjecture Let
be a
-connected cubic graph and let
be a
-regular subgraph such that
is connected. Then
has a cycle double cover which contains
(i.e all cycles of
).








Keywords:
3-Decomposition Conjecture ★★★
Author(s): Arthur; Hoffmann-Ostenhof
Conjecture (3-Decomposition Conjecture) Every connected cubic graph
has a decomposition into a spanning tree, a family of cycles and a matching.

Keywords: cubic graph
Strong 5-cycle double cover conjecture ★★★
Author(s): Arthur; Hoffmann-Ostenhof
Conjecture Let
be a circuit in a bridgeless cubic graph
. Then there is a five cycle double cover of
such that
is a subgraph of one of these five cycles.




Keywords: cycle cover
