Conjecture Can all problems that can be computed by a probabilistic Turing machine (with error probability < 1/3) in polynomial time be solved by a deterministic Turing machine in polynomial time? That is, does P = BPP?
Conjecture For every graph without a bridge, there is a flow .
Conjecture There exists a map so that antipodal points of receive opposite values, and so that any three points which are equidistant on a great circle have values which sum to zero.
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.
Question Is the MSO-alternation hierarchy strict for pictures that are balanced, in the sense that the width and the length are polynomially (or linearly) related.
Conjecture If is the adjacency matrix of a -regular graph, then there is a symmetric signing of (i.e. replace some entries by ) so that the resulting matrix has all eigenvalues of magnitude at most .
Conjecture If is a bridgelesscubic graph, then there exist 6 perfect matchings of with the property that every edge of is contained in exactly two of .
Let be a class of finite relational structures. We denote by the number of structures in over the labeled set . For any class definable in monadic second-order logic with unary and binary relation symbols, Specker and Blatter showed that, for every , the function is ultimately periodic modulo .
Question Does the Blatter-Specker Theorem hold for ternary relations.
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is a connected graph on 
vertices, then 
for 
. 
-degenerate graph (a forest) and a 
-degenerate graph is 
-colourable. 
denote ''
divides 
''. The mimic function in number theory is defined as follows [1].
divisible by 
, the mimic function, 
, is given by,
is defined to be the mimic number of any positive integer 
. 
, there is only a finite number of good-edge-labeling critical graphs with average degree less than 
. 
for reloid 
. 
for every funcoid 
(see below mentioned online article).
can be represented as the sum of an odd prime number and an odd 
.
so that antipodal points of 
receive opposite values, and so that any three points which are equidistant on a great circle have values which sum to zero. 
, there is a constant 
(possibly 
) so that the union (as multisets) of any 
contains an additive basis. 
? 
, such that 
.
and 
are 
is the adjacency matrix of a 
-regular graph, then there is a symmetric signing of 
entries by 
) so that the resulting matrix has all eigenvalues of magnitude at most 
. 
has chromatic number at most 
. 
concentrated on a single value? 
, then 
cycles of length 
. 
of 
for some filter objects 
, 
. Particularly, is this formula true for 
? 
for some filter objects 
be a class of finite relational structures. We denote by 
the number of structures in 
. For any class 
, the function 
, for 
if each of the color classes is of size of either 
or 
? 
there is 
such that, for every large 
such that 
and 
. 
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