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 ).
A covering design, or covering, is a family of -subsets, called blocks, chosen from a -set, such that each -subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by .
Problem Find a closed form, recurrence, or better bounds for . Find a procedure for constructing minimal coverings.
Question Is the binary affine cube the only 3-connected matroid for which equality holds in the bound where is the circumference (i.e. largest circuit size) of ?
Conjecture Let be a sequence of points in with the property that for every , the points are distinct, lie on a unique sphere, and further, is the center of this sphere. If this sequence is periodic, must its period be ?
Problem Let be an indexed family of filters on sets. Which of the below items are always pairwise equal?
1. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the reloidal product of filters .
2. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the starred reloidal product of filters .
Conjecture Let is a family of multifuncoids such that each is of the form where is an index set for every and is a set for every . Let every for some multifuncoid of the form regarding the filtrator . Let is a graph-composition of (regarding some partition and external set ). Then there exist a multifuncoid of the form such that regarding the filtrator .
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 Let be an eulerian graph of minimum degree , and let be an eulerian tour of . Then admits a decomposition into cycles none of which contains two consecutive edges of .
login/create account
-graph if it has a bipartition 
so that every vertex in 
has degree 
and every vertex in 
has degree 
. 
be a matroid of rank 
, and for 
let 
be the number of closed sets of rank 
.
is unimodal. 
. 
be a 
-connected cubic graph and let 
be a 
is connected. Then 
covering design, or covering, is a family of 
-subsets, called blocks, chosen from a 
-set, such that each 
-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by 
.
. Find a procedure for constructing minimal coverings. 
the only 3-connected matroid for which equality holds in the bound 
where 
is the circumference (i.e. largest circuit size) of 
be a prime natural number. Find all primes 
, such that 
.
verices has an induced forest with at least 
vertices. 
-size circuits compute the function 
on 
defined inductively by 
, 
, 
, and 
? 
, there is an integer 
so that every strongly 
be a sequence of points in 
with the property that for every 
, the points 
are distinct, lie on a unique sphere, and further, 
is the center of this sphere. If this sequence is periodic, must its period be 
? 
be an indexed family of filters on sets. Which of the below items are always pairwise equal?
. 
, whether there exists a homomorphism from 
for some constant 
? 
is a family of multifuncoids such that each 
is of the form 
where 
is an index set for every 
is a set for every 
. Let every 
for some multifuncoid 
of the form 
regarding the filtrator 
. Let 
). Then there exist a multifuncoid 
of the form 
such that 
regarding the filtrator 
. 
so that the power series 
is bounded for all 
. 
, where 
denotes the oddness of the graph 
always rational? 
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)
-
of 
so that 
is 
-edge-connected and 
is 
-edge-connected? 
, and let 
be an eulerian tour of 
has chromatic number at most 
.
has a homomorphism to 
. 
Drupal
CSI of Charles University