The deck of a graph is the multiset consisting of all unlabelled subgraphs obtained from by deleting a vertex in all possible ways (counted according to multiplicity).
Conjecture If two graphs on vertices have the same deck, then they are isomorphic.
Conjecture For all there is an integer such that every digraph of minimum outdegree at least contains a subdivision of a transitive tournament of order .
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.
Conjecture Let be a finite family of finite sets, not all empty, that is closed under taking unions. Then there exists such that is an element of at least half the members of .
Problem has the homotopy-type of a product space where is the group of diffeomorphisms of the 4-ball which restrict to the identity on the boundary. Determine some (any?) homotopy or homology groups of .
Conjecture If in a bridgeless cubic graph the cycles of any -factor are odd, then , where denotes the oddness of the graph , that is, the minimum number of odd cycles in a -factor of .
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.
Conjecture If every second positive integer except 2 is remaining, then every third remaining integer except 3, then every fourth remaining integer etc. , an infinite number of the remaining integers are prime.
Conjecture Let be a complex projective variety. Then every Hodge class is a rational linear combination of the cohomology classes of complex subvarieties of .
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is the multiset consisting of all unlabelled subgraphs obtained from 
vertices have the same deck, then they are isomorphic. 
-chromatic graph on at most 
vertices, then 
. 
and graph 
. 
. 
, the number of even latin squares of order 
always rational? 
such that every digraph of minimum outdegree at least 
is called a Diophantine 
-tuple if 
is a perfect square for all 
. 
is a Diophantine quadruple and 
, then 
-manifold has the homotopy type of the 
, is it diffeomorphic to 
is a connected cubic graph admitting a 
-edge coloring. Then there is an edge 
such that the cubic graph homeomorphic to 
has a 
on an even number of vertices can be decomposed into 
directed paths. 
, for 
a large prime, always contain a rainbow 
if each of the color classes is of size of either 
or 
? 
rectangular 
inside an 
? 
be a finite family of finite sets, not all empty, that is closed under taking unions. Then there exists 
such that 
denote the 
? 
has chromatic number at most 
. 
has the homotopy-type of a product space 
where 
is the group of diffeomorphisms of the 4-ball which restrict to the identity on the boundary. Determine some (any?) homotopy or homology groups of 
for some constant 
? 
? 
is a sequence of elements from a multiplicative group of order 
so that 
. 
-factor are odd, then 
, where 
denotes the oddness of the graph 
(possibly 
) so that the union (as multisets) of any 
contains an additive basis. 
has a Hamilton cycle. 
be a complex projective variety. Then every Hodge class is a rational linear combination of the cohomology classes of complex subvarieties of 
has a cycle with length at most 
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