Conjecture Let be a graph and let such that for any pair there are edge-disjoint paths from to in . Then contains edge-disjoint trees, each of which contains .
Conjecture There is an integer-valued function such that if is any -connected graph and and are any two vertices of , then there exists an induced path with ends and such that is -connected.
Let be a simple graph, and for every list assignment let be the maximum number of vertices of which are colorable with respect to . Define , where the minimum is taken over all list assignments with for all .
Conjecture [2] Let be a graph with list chromatic number and . Then
Conjecture Let be an integer. For every integer , there exists an integer such that for every digraph , either has a pairwise-disjoint directed cycles of length at least , or there exists a set of at most vertices such that has no directed cycles of length at least .
Conjecture For every , the sequence in consisting of copes of and copies of has the fewest number of distinct subsequence sums over all zero-free sequences from of length .
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?
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be a graph and let 
such that for any pair 
there are 
edge-disjoint paths from 
to 
in 
edge-disjoint trees, each of which contains 
. 
, for 
a large prime, always contain a rainbow 
if each of the color classes is of size of either 
or 
? 
, there exist positive integers 
, 
, 
such that 
.
denote the pebbling number of a graph 
. 
such that if 
with ends 
is 
be integers. Set 
and 
for 
. Eventually we have 
; put 
.
, since 
, 
, 
, 
, 
, 
, 
, 
.
.
are invertible 
matrices with entries in 
for a prime 
submatrix 
of ![$ [B_1 B_2 \ldots B_p] $](/files/tex/86661dc2948aeca789b4392c2e2a9cbf7d96f735.png)
so that 
which is slice, is it a ribbon knot?
is unfriendly if every vertex has at least as many neighbors in the other classes as in its own. 
let 
be the maximum number of vertices of 
, where the minimum is taken over all list assignments 
for all 
. 
and 
. Then ![\[\frac{\lambda_r}{r}\geq\frac{\lambda_s}{s}.\]](/files/tex/47be18e956355dd433b88b66eabf01a9e3ed5f61.png)
for some filter objects 
, 
. Particularly, is this formula true for 
? 
for some filter objects 
-graph if it has a bipartition 
so that every vertex in 
and every vertex in 
has degree 
. 
be an integer. For every integer 
, there exists an integer 
such that for every digraph 
, either 
pairwise-disjoint directed cycles of length at least 
, or there exists a set 
vertices such that 
has no directed cycles of length at least 
, the sequence in 
consisting of 
copes of 
and 
copies of 
has the fewest number of distinct subsequence sums over all zero-free sequences from 
. 
exist a 
be a set of ![\[m(A) = - \min_x \sum_{a \in A} \cos(ax).\]](/files/tex/7a772ebd0b7fd98eeab7fda3a5e9674b1dc4c984.png)
What is 
? 
is a sequence of elements from a multiplicative group of order 
so that 
. 
. The representation function 
for 
. We call 
is never 
.
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