If , are graphs, a function is called cycle-continuous if the pre-image of every element of the (binary) cycle space of is a member of the cycle space of .
Problem Does there exist an infinite set of graphs so that there is no cycle continuous mapping between and whenever ?
Conjecture For every set of points in the plane, not all collinear, there is a point in contained in at least lines determined by , for some constant .
Let be a hypergraph. A strongly maximal matching is a matching so that for every matching . A strongly minimal cover is a (vertex) cover so that for every cover .
Conjecture If is a (possibly infinite) hypergraph in which all edges have size for some integer , then has a strongly maximal matching and a strongly minimal cover.
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 .
We say that a set is -universal if every vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in , and all edges are (non-intersecting) straight line segments.
Question Does there exist an -universal set of size ?
Let be a positive integer. We say that a graph is strongly -colorable if for every partition of the vertices to sets of size at most there is a proper -coloring of in which the vertices in each set of the partition have distinct colors.
Conjecture If is the maximal degree of a graph , then is strongly -colorable.
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,
are graphs, a function 
is called cycle-continuous if the pre-image of every element of the (binary) cycle space of 
so that there is no cycle continuous mapping between 
and 
whenever 
? 
let 
. 
be a matroid on 
, let 
be a map, put 
and 
. Then 
of 
points in the plane, not all collinear, there is a point in 
lines determined by 
. 
-regular directed graph with no parallel arcs, then 
arc-disjoint directed cycles. 
does there exists a 
such that every graph with average degree smaller than 
are simple finite graphs, then 
. 
is the 
paths. 
satisfy 
. Then the elements of 
and 
may be ordered 
and 
so that the sums 
are pairwise distinct. 
so that 
for every matching 
. A strongly minimal cover is a (vertex) cover 
so that 
for every cover 
. 
for some integer 
. 
be an integer and let 
. Then either 
minor for some 
or 
such that 
meets 
in at most one vertex, 
. 
, the sequence in 
consisting of 
copes of 
and 
copies of 
has the fewest number of distinct subsequence sums over all zero-free sequences from 
. 
and 
are 
is 
? 
be a positive integer. We say that a graph 
is the maximal degree of a graph 
-colorable. 
edges whose deletion destroys every triangle. 
contains every oriented tree of order 
. Does the fragment 
have the finite model property? 
be integers. Set 
and 
for 
. Eventually we have 
; put 
.
, since 
, 
, 
, 
, 
, 
, 
, 
.
.
of co-prime positive integers 
for 
. 
, there is an integer 
so that every strongly 
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