
Kriesell's Conjecture ★★
Author(s): Kriesell
Conjecture Let
be a graph and let
such that for any pair
there are
edge-disjoint paths from
to
in
. Then
contains
edge-disjoint trees, each of which contains
.










Keywords: Disjoint paths; edge-connectivity; spanning trees
2-colouring a graph without a monochromatic maximum clique ★★
Conjecture If
is a non-empty graph containing no induced odd cycle of length at least
, then there is a
-vertex colouring of
in which no maximum clique is monochromatic.




Keywords: maximum clique; Partitioning
Distributivity of a lattice of funcoids is not provable without axiom of choice ★
Author(s): Porton
Conjecture Distributivity of the lattice
of funcoids (for arbitrary sets
and
) is not provable in ZF (without axiom of choice).



A similar conjecture:
Conjecture
for arbitrary filters
and
on a powerset cannot be proved in ZF (without axiom of choice).



Keywords: axiom of choice; distributive lattice; distributivity; funcoid; reverse math; reverse mathematics; ZF; ZFC