Problems

If D is a dimatroid and C,D ∈ D , then there exist C',D'∈ D of almost equal size whose union is C ∪ D .

For each vertex v in a graph G of order n ≥ 4, b(G-v)=b(G)+lfloorn/2⌋-2 if and only if G=C_4,P_4,2P_2

In the general case, for any m > 1, n = 2^m, for any n-tuple of A matrices satisfying (1), does there always exist an n-tuple of B matrices of order c that satisfies construction (H0) under condition (H1), where c = M(n-1), with M defined…

For 0<α≤ 1 , among all trees, characterize the tree which has the maximum generalized distance spectral radius.

Can we find the minors for this property?

Open problem: • d∈0,2 for n>7

Pascal-type behavior except for the entry 14.

If we remove the equal coefficients condition, does Theorem 4.1 hold with n = d + 1?

(i) For every triangulation K of a Witt space with vanishing middle intersection homology GIN(K) ⊂ GIN(C(d,n)). (2.1) (ii) The strong upper bound conjecture holds for arbitrary polyhedral complexes (and even for all regular cell complexes…

Is there some C(r)>2 such that ρ_2(2(r+2)+1,r+2)≥C(r)ρ_2(2r+1,r) holds for all r ≥2 ?

Suppose G is a Hamiltonian chordal graph. Is G cycle extendable if min{Δ(T) : (T, T) is a tree decomposition for G} = 4?

It seems an interesting problem to characterize semisymmetric graphs with Wiener dimension 2.

Could it be true that for any finite dimensional \mathfrak{gl}{n} -module W there exists a polynomial p{W}(t)(p_{W}(t)=t ??) such that for all partitions \pi and \mu one has if a_{N \mu,W}^{N \pi}\ge p_{W}(N) , then a_{\mu,W}^{\pi}\ne 0 .

Characterize the graphs G such that every irreducible dominating set in G is either a minimal dominating set or a minimal total dominating set.

CONNECTED TREEWIDTH can be solved by an O(n^f(k))-time algorithm.

Let d ∈ [0, n] and E ⊆ [0, n]. For j ∈ [0, n], if j ∉ Z-cl_n,d(E), then there exists a polynomial P(X) = ℓ_1(X) … ℓ_k(X)σ(X) ∈ F_p[X], where deg ℓ_1 = … = deg ℓ_k = 1, and σ(X) is a symmetric polynomial, such that deg P ≤ d, P|_underlinei…

It remains unknown to us whether or not there exists a divisional but not inductive poset among non-lattice, locally geometric posets.

For positive integers k, d and n with k ≥3, find the largest value f_{k,d}(n) such that every connected graph G of maximum degree at most d and of order n contains a k-tree T with |T|≥f_{k,d}(n).

If G is a critical graph (not banned) and ρ^⊥(G)=d , then G-M(G) (with M a match maximal) has ρ^⊥(G-M(G))≤ d-1

Can one prove better upper or lower bounds for ℓ_n ?