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Does there exist a graph Γ of order n and level of symmetry equal to n-k/n for arbitrarily large k ≥2 ?

Let S be the parameter matrix of a k-transversal in a d-uniform r-regular hyper graph G. Then the characteristic polynomial of S is φ(λ)=λ^d-2∏_i=j^d(λ-ξ^jkr), where ξ is a d-th primitive root of unity.

Let λ be a Young diagram. Then [∅, λ] has the CDE property if and only if λ is balanced (of any slope).

For every tree T of order at least 3, overlinemc(T) ≤ 3.

Let m ≥ 3 be an integer, and let Γ be a graph coprime to K_m such that Aut(Γ) ≠ 1. If Γ is connected and R-thin, then (Γ, K_m) is stable.

For k=1,2, there exist P^(5)(k,10-k) -designs of order v if and only if: v ≥ 10-k and v ≡ 1bmod 8 or v ≡ 3bmod 8 .

Find the asymptotics of the maximizing index of E_r(n,k) .

Characterize the nontrivial lexicographic product graphs that are well-totally-dominated.

Is there a 2-factor in B_3 in which all cycles have length of at most 10?

We conjecture that this ring is Z⟨c,d,fracc^2k+1-e^2k+12⟩.

Let G be a bipartite digraph with sides A and B. For a set X ⊆ A let N^↔(X) denote the set of vertices, which have an edge to and from X. If |N^↔(X)| ≥ |X| - 1 holds for every X ⊆ A, then there exists a directed path that covers A.

For any n ≥3, the polynomial (x+1)A_n-1(x)+kx A_n-2(x) is Hurwitz stable if and only if k>-2E_n/E_n-1 .

lim_l → ∞ limsup_n → ∞ P_n^av(τ)(A_l;k_n^(n)) = 0, for all τ ∈ ∪_m=2^∞ S_m and for all k_n.

they conjectured that C_m × P_n is SEAT if m ≥ 4 even, n ≥ 3 and d ∈ 0, 2;

If G is a graph with maximum degree Δ(G) and k ≥ 2, then la_k(G) ≤ ⌈ Δ(G) · |V(G)|/2 ⌊ k|V(G)|/k+1 ⌋ ⌉, when Δ(G) = |V(G)| - 1, ⌈ Δ(G) · |V(G)| + 1/2 ⌊ k|V(G)|/k+1 ⌋ ⌉, when Δ(G) < |V(G)| - 1.

Let H be a hypertree. Then X_H is F-positive.

For every K_r -free graph G, fracα(G)overlineα_G(1)≥ 1+1/r. For every K_r -free graph G of minimum degree d, fracα(G)overlineα_G(1)≥ 2-o_d(1), with r fixed as d →∞ .