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Thus we can ask a question: "Can we develop an enumeration method to find the number of perfectly dominated trees of order n?"

the existence of such an f has been proved, but uniqueness in T_0 has not.

Our result leaves open the question about the largest cardinality of a set of pairwise completely K-different permutations.

Let G be a connected graph of order n. Then G is a star graph if and only if n_0(e;k)=n_u(e;k)=0,n_v(e;k)=( cn-2k-1 ) or n_0(e;k)=n_v(e;k)=0,n_u(e;k)=( cn-2k-1 ) for any edge e=uv ∈ E(G) .

Let G be a Hamiltonian bipartite graph of minimum degree δ on n vertices, where n<2(δ^{2}-δ+1) . Then G has a cycle of length 2 l for each integer l, 2 ≤ l ≤ n / 2.

For some fixed n, the POLYTOPE TRANSLATION problem for rational simplices Δ ⊂R^n is NP-hard.

If C is a nondegenerate hyperplane code, does T_C have a quadratic Gröbner basis? Does it have a quadratic generating set?

There exist constants K_1 and K_2 such that for every pair of integers m and n, where m ≥ K_1 and n ≥ K_2, we have χ_st'(C_m square P_n) = 6.

We don't think that our bound on the number of k-rich Möbius functions is tight. On the contrary, we conjecture that the right side can be replaced by O(n^4/k^3) in this case too.

This raises the question of how sparse a graph can be for the last Theorem to remain true.

Let (X,B,μ) be a σ -finite measure space and T:X → X a measure preserving transformation. If A ∈B , then there exists n ∈N with μ(A ∩ T^-nA ∩ T^-2nA ∩… ∩ T^-ℓ nA)>0,or (5) μ(T^-inA ∩ T^-jnA)=0 ∀0 ≤ i<j ≤ℓ. (6)

I.e., for hereditary property H, what are the maximal properties H' ⊇ H such that d^*(H') = d^*(H)?

Full characterization/ Examples of strongly minimal k-vertex-rigid graphs in three-space or higher dimensions.

However, it is unknown whether all finite groups are connected 3-CI-groups, and it is conjectured in [15] that the answer is positive.

What is the computational complexity of ~?

If G is a 3-edge-connected plane graph with L(G)=5, then fer(G)=L(G)+1.

What about Wilf equivalence in [m]^* where [m] = 1, 2, …, m? ... Is it true that u ~_m v if and only if u ~ v?

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.