Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
348 problems
Ehrhart equivalence is a necessary and sufficient condition for (not necessarily finite or rational) discrete equidecomposability.
Is it true that for every nonnegative integer k, there exists a connected graph G satisfying φ(G) − κ(G) + 1 = k?
Is there a nice combinatorial proof for the number of interior lattice points of P_n(132,312) ?
We discuss ... including some new ones that we present in this last section (in particular Conjectures 11.3 and 11.5).
Can Theorem 4.2 be true for dimension ≥ 4 ?
We conjecture that the necessary conditions are sufficient in general, except eventually for a few values (for example it can be shown that K_{4,4,4,1} cannot be decomposed into K_4's).
W(n,k,4)=0 if either (i) n<14 or (ii) n=14,k<14.
Do either the height 1 or Hilbert basis extensions generate the same poset Cones(d)?
We conjecture that if a Γ -degree sequence d' has a tree realization then each such a realization of d' has the same number of pendant vertices.
If D is a digraph of order n, then d_I(D) + d_I(barD) ≤ n + 1.
For all primitive digraphs G such that G ≠ K_n^*, exp(G)/l(G) ≥ 2.
The construction described above has Ω(n^6) crossings. Does there exist a cycle of small area in every drawing of K_n such that every pair of edges intersect a constant number of times?
What is the smallest n for which Φ_n(G,H)= r(G, H)-2 ? Does this relation hold for all n ≥r(G, H) ?
For every weakly distance-regular digraph Γ with valency k, the edge connectivity equals to k. Moreover if k > 2, any minimum edge cut is the set of all edges going into (or coming out of) a single vertex.
The set E_n is a minimal generating set in the strong sense: E_n has the lowest cardinality of any generating set of C_n .
If G is a connected graph containing a percolating set which r-percolates in k rounds and r ≥2, then k≤ diam_D(G) .
The complete graph possesses the largest eigen-cover area of all classes of graphs.
Does it make a difference if for every vertex v on level i we also prescribe a connected component of {(x, y, z) ∈ R^3 | z = i} ∩ S to which v belongs in a drawing?
We noticed how similar these are to the asymptotics of the sequences enumerating 123-avoiding words with r occurrences of each letter, given on page 8 of [SZ], and we have a similar conjecture as on page 3 of [SZ] that a_r(n) is…
does there exist a packing k-colouring so that, for i<j ≤ k the asymp-totic frequency of colour i is no more than the asymptotic frequency of j?