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.
4 problems
Let G' be a graph obtained from a (Δ,1) -bidegreed graph G by inserting a bouquet in an edge of a bouquet internal path. Then (i) if ρ(G)<1+√Δ-1, then ρ(G^′)>ρ(G); (ii) if ρ(G)>1+√Δ-1, then ρ(G^′)<ρ(G); (iii) if ρ(G)=1+√Δ-1, then…
Let Y and Z be t-cross-intersecting sets in G_n whose sizes meet the bound in Theorem 1.2. If n is sufficiently large compared to t, then Y = Z and Y or Y^T is a t-coset.
(Brill-Noether Existence for ℝ-Divisors on Graphs) Let ρ(g,r,d)=g-(r+1)(g-d+r). Fix two real numbers r ≥0, 2 g-2 ≥d. If ρ(g,r,d)≥0 then there exists an ℝ-divisor of degree at most d and rank equal to r on G.
(Covering Radius Conjecture) Let λ ∈ [1/g, g] (recall that g ≥ 1). The covering radius of N_G with respect to the polytope P_{1,λ} is at least √(g/λ)/n where n is the number of vertices of G.