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L_2(3),overlineL_2(3),G_0,barG_0 are the only regular graphs for which equality holds in the above inequality.

it is still unknown a connected non-graceful graph that has a vertex relaxed graceful labelling.

For a pr-graph H, the following are equivalent. (i) B_H has no invertible pairs or chains. (ii*) B_H has a parity-symmetric special bipartite-min ordering. (iii) S_H has a semi-conservative WNU-polymorphism.

Do trees of maximum degree at most 4 have exponentially independent sets of linear order?

However, this formula is not particularly useful unless the least integer K such that the MDGP will hold for all k ≥K can be determined. The calculation of this tight bound for a given graph remains an open question.

If all degrees of G are even, then for any two partitions T_1,T_2 of T, the vertices of Q(G,T_1)∩ Q(G,T_2) are T_1-T_2 -feasible, i.e. Q(G,T_1)∩ Q(G,T_2) is the convex hull of T_1-T_2 -feasible vectors.

If F →(nG) , then must F contain at least lfloorr(nG)/|V(G)|⌋ copies of G?

The problem COMPUTECHARBINARY is GapP-complete under many-one reductions.

If the linear compression dimension of S is given by log_{2}(|S|)+o(n) (hence matches the non-linear compression dimension) then S is contained in the union of 2^{o(n)} translates of some subspaces of size at most |S|.

Let K be a clarified formal context with |SRB_k(K)|=n . Then |SOB_k(B(K))|≥ n holds.

This results lead us to establish a conjecture that gives us an algebraic and a combinatorial description of the sandpile group of the cone of the hypercube Q_d of dimension d. More precisely, K(c(Q_d)) ≅ bigoplus_i=1^d Z_2i+1^binomdi =…

(i) For each p ≥ 6, γ_p^(2) > γ_p^(3) and γ_p^(3) < γ_p^(4) < … < γ_p^(p-1). (ii) For each p ≥ 7, Γ_p^(2) > Γ_p^(3) (which is the same as γ_p^(2) > γ_p^(3)), and Γ_p^(3) < Γ_p^(4) < … < Γ_p^(p-1).

For any integer ℓ ≥ 4, there is a constant c_ℓ such that rwsat(n, C_ℓ) = 3/2n + c_ℓ.

Can we generalize the property K_n+1∈ K_n,K_n+1 to the Whitney- and r-Whitney numbers?

If G=(V, E) is self-complementary and vertice-transitive,then ρ^⊥(G)=⌈ n/2 ⌉

Let n_1 ≥ n_2 ≥ … ≥ n_t ≥ 4 be positive integers such that at most one of n_2, n_3, …, n_t is odd. Then R(P_n_1, P_n_2, …, P_n_t) = n_1 + ∑_i=2^t (⌊ n_i/2 ⌋ - 1).

Suppose that the graphs Γ_1 and Γ_2 have the same refined spectra. Are their complements cospectral?

Can Theorem 1.3 and Theorem 2.11 be generalized to signed tropical convexity?

χ(2d,d+1)=d+2.

Give a sharp upper bound on γ(X(G)) in terms of γ(G) for any connected graph G with δ(G) ≥ 2, where γ denotes the domination number.