Conjecture   In the category of continuous funcoids (defined similarly to the category of topological spaces) the following is a direct categorical product:

\item Product morphism is defined similarly to the category of topological spaces. \item Product object is the sub-atomic product. \item Projections are sub-atomic projections.

Question   Are there graphs for which is arbitrarily large?

Problem   Are almost all graphs uniquely determined by the spectrum of their adjacency matrix?

Conjecture   If is the adjacency matrix of a -regular graph, then there is a symmetric signing of (i.e. replace some entries by ) so that the resulting matrix has all eigenvalues of magnitude at most .

Conjecture  (BEC-conjecture)   If and are -vertex graphs and , then and pack.

Conjecture   Every k-arc-strong tournament decomposes into k spanning strong digraphs.

Question   Is there a polynomial time approximation scheme for the feedback arc set problem for the class of tournaments?

Problem   Let be positve integer Does there exists an integer such that every -strong tournament admits a partition of its vertex set such that the subtournament induced by is a non-trivial -strong for all .

Conjecture   There is an absolute constant such that for every hexagonal graph and vertex weighting ,

Conjecture   Let be a planar graph of maximum degree . The chromatic number of its square is

\item at most if , \item at most if , \item at most if .

Conjecture   There is a constant such that the list chromatic number of any bipartite graph of maximum degree is at most .

Conjecture   Every prism over a -connected cubic planar graph can be decomposed into two Hamilton cycles.

Conjecture   Every simple -uniform hypergraph on vertices which contains no complete -uniform hypergraph on four vertices has at most hyperedges.

Conjecture   Every simple -uniform hypergraph on vertices which contains no complete -uniform hypergraph on five vertices has at most hyperedges.

Conjecture   Every -connected graph with a Hamilton cycle has a second Hamilton cycle.

Conjecture   If is a -connected planar graph, then has a Hamilton cycle.

Conjecture   Every digraph in which each vertex has outdegree at least contains directed cycles such that meets in at most one vertex, .

Conjecture   For every , there is an integer so that every strongly -connected tournament has edge-disjoint Hamilton cycles.

Conjecture   For , every -diregular oriented graph on at most vertices has a Hamilton cycle.

Question   Are there any switching-nonreconstructible digraphs on twelve or more vertices?

Conjecture   Every simple graph on five or more vertices is switching-reconstructible.