Esmeralda Nastase

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A subspace partition of P = PG(n, q) is a collection of subspaces of P whose pairwise intersection is empty. Let σq(n, t) denote the minimum size (i.e., minimum number of subspaces) in a subspace partition of P in which the largest subspace has dimension t. In this paper, we determine the value of σq(n, t) for n ≤ 2t + 2. Moreover, we use the value of σq(2t(More)
A subspace partition Π of V = V (n, q) is a collection of subspaces of V such that each 1-dimensional subspace of V is in exactly one subspace of Π. The size of Π is the number of its subspaces. Let σ q (n, t) denote the minimum size of a subspace partition of V in which the largest subspace has dimension t, and let ρ q (n, t) denote the maximum size of a(More)
A graph G is (k + 1)-critical if it is not k-colourable but G− e is k-colourable for any edge e ∈ E(G). In this paper we show that for any integers k ≥ 3 and ℓ ≥ 5 there exists a constant c = c(k, ℓ) > 0, such that for allñ, there exists a (k + 1)-critical graph G on n vertices with n > ˜ n and odd girth at least ℓ, which can be made (k − 1)-colourable only(More)
A graph G is chromatically k–connected if every vertex cutset induces a subgraph with chromatic number at least k. Thus, in particular each neighborhood has to induce a k–chromatic subgraph. In [3], Godsil, Nowakowski and Nešetřil asked whether there exists a k–chromatically connected graph such that every minimal cutset induces a subgraph with no(More)
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