Conjecture There exists an integer such that every -arc-strong digraph with specified vertices and contains an out-branching rooted at and an in-branching rooted at which are arc-disjoint.
Conjecture There exists a fixed constant so that every abelian group has a subset with so that the Cayley graph has no clique or independent set of size .
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.
Problem What is the largest connected planar graph of minimum degree 3 which has everywhere positive combinatorial curvature, but is not a prism or antiprism?
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 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 ).
Conjecture For , let be the statement that given any exact -coloring of the edges of a complete countably infinite graph (that is, a coloring with colors all of which must be used at least once), there exists an exactly -colored countably infinite complete subgraph. Then is true if and only if , , or .
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.
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 .
For and positive integers, the (mixed) van der Waerden number is the least positive integer such that every (red-blue)-coloring of admits either a -term red arithmetic progression or an -term blue arithmetic progression.
The famous 0-1 Knapsack problem is: Given and integers, determine whether or not there are values so that The best known worst-case algorithm runs in time times a polynomial in . Is there an algorithm that runs in time ?
Problem Consider the set of all topologically inequivalent polyhedra with edges. Define a form parameter for a polyhedron as where is the number of vertices. What is the distribution of for ?
login/create account
contains a directed path of length 
. 
for every filter objects 
and 
and a funcoid 
? 
has chromatic number at most 
.
be a loopless multigraph. Then the edge chromatic number of 
with specified vertices 
and 
contains an out-branching rooted at 
so that every abelian group 
with 
so that the 
has no clique or independent set of size 
. 
there is an integer 
such that every set of at least 
collinear points or an empty hexagon. 
, determine whether or not 
, then there is a 
-vertex colouring of 
. 
-degenerate graph (a forest) and a 
is not an integer. 
be a 
is connected. Then 
be an integer and let 
denote the least integer 
spanning trees. Then 
is the only ![\[ M_n = 2^p - 1 \]](/files/tex/eb18a56e5c2e8b1be6ac733d217c0c1f1a47a94e.png)
that is prime.
is an invertible 
matrix, then there is an 
of ![$ [A A] $](/files/tex/d1e9d82c656535b507686183e640178057fae455.png)
so that 
is nonzero. 
-manifold has the homotopy type of the 
, is it diffeomorphic to 
is the minimum number 
for which there exists a polytope 
with 
with 
.
? 
, let 
be the statement that given any exact 
-coloring of the edges of a complete countably infinite graph (that is, a coloring with 
-colored countably infinite complete subgraph. Then 
, 
, or 
.
and a function 
such that if 
, then every saturated 
has cardinality at least 
? 
-connected finite graph, is there an assignment of lengths 
to the edges of 
is a connected cubic graph admitting a 
such that the cubic graph homeomorphic to 
has a 
be an indexed family of filters on sets. Which of the below items are always pairwise equal?
. 
is the least positive integer ![$ [1,n] $](/files/tex/661d0acc09fbc5b62f49645a71cf7d831a26563f.png)
admits either a 
, 
. 
and 
integers, determine whether or not there are 
values 
so that 
The best known worst-case algorithm runs in time 
times a polynomial in 
?
where 
for 
? 
Drupal
CSI of Charles University