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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.

(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).

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.

An interesting open question is whether L(p, 1)-LABELING parameterized by only twin cover number is FPT or not.

Suppose n = n_1 + … + n_d and k ≥ k_1 + … + k_d, where n_i > k_i ≥ 0 are integers. Let X_1 ∪ … ∪ X_d be a partition of [n] with |X_i| = n_i, and H := F ⊆ binom[n]k : |F ∩ X_i| ≥ k_i for i = 1, …, d . If n_i ≥ 2k_i for all i and n_i > k -…

Charactrize all graphs G which diam(G)=2 and diam(D_{2}(G))=2 or 3.

Do there exist polynomials f_{1}(\zeta),f_{2}(\zeta),f_{3}(\zeta) and f_{4}(\zeta) in \zeta of order 6 , given as in (15), satisfying (16) and (17), such that f_{1}(1)=0,\quad f_{2}(1)^{2}=f_{3}(1)^{2}=f_{4}(1)^{2}=3^{2}?

Let n,r_1,...,r_m∈ Z^+ with r_1+… +r_m≡ 1(bmod 2) and j ∈N , there holds∑_k=0^nη_k∏_i=1^mA_n+i-1,k(q)^r_i≡ 0 bmod 1/[n+1][ c2n n ],where η_k=q^j(k^2+k) or η_k=(-1)^kq^( ck+12 )+j(k^2+k) .