Suppose is a finite group, and is a positive integer dividing . Suppose that has exactly solutions to . Does it follow that these solutions form a subgroup of ?
Conjecture It has been shown that a -outerplanar embedding for which is minimal can be found in polynomial time. Does a similar result hold for -edge-outerplanar graphs?
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 \item If is a 4-edge-connected locally finite graph, then its line graph is hamiltonian. \item If the line graph of a locally finite graph is 4-connected, then is hamiltonian.
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has an acyclic induced subdigraph of order at least 
. 
is the total graph of a multigraph, then 
. 
such that 
are prime.
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 
. 
is 
to be the maximum degree, 
to be the size of the largest 
to be the chromatic number of 
for every graph 
-
(mod 
) for every vertex 
. 
. Suppose that 
. Does it follow that these solutions form a subgroup of 
-connected graph with a Hamilton cycle has a second Hamilton cycle. 
? 
-diregular if every vertex has indegree and outdegree at least 
, every 
vertices has a Hamilton cycle. 
be an integer and let 
denote the least integer 
be a 
, there exist positive integers 
, 
, 
such that 
.
be the unique integer (with respect to a fixed 
) such that
is a prime iff ![$$ \displaystyle \sum_{i=1}^{\left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor} r_i = \left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor $$](/files/tex/99af565f4cc4d3bab11eb3fbf54f78626678d484.png)
for principal funcoid 
and a set 
of funcoids of appropriate sources and destinations. 
.
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. 
of a locally finite graph 
, then 
, then 
cycles of length 
. 
are independent random variables with ![$ \mathbb{E}[X_i] \leq \mu $](/files/tex/e0268221532981debea25e9446c8ee6f112e1881.png)
, then ![$$\mathrm{Pr} \left( \sum X_i - \mathbb{E} \left[ \sum X_i \right ] < \delta \mu \right) \geq \min \left ( (1 + \delta)^{-1} \delta, e^{-1} \right).$$](/files/tex/03dc1130142ee6fefcc33888e2fb6137211bf327.png)
be an abelian group. Is the 
the following inequality holds 
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