In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k − 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983. We verify it for the next case, by proving that every digraph with minimum out-degree at least five contains three disjoint cycles. To show this, we improve Thomassen’s result b...

The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r−1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r = 2, and very recently the conjecture was proved for the case where r = 3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we pre...

Let D be the triangle with attached edge (i. e. D is the graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). J.C. Bermond and J. Schönheim [1], proved that a D-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial D-design of order n, n ≥ 8, and let V ⊂ W , |V | = v < n. We say that a handcuffed design (V,P) of order v and b...

3 For d, k ∈ N with k ≤ 2d, let g(d, k) denote the infimum density of binary 4 sequences (xi)i∈Z ∈ {0, 1}Z which satisfy the minimum degree condition d ∑ j=1 (xi+j + 5 xi−j) ≥ k for all i ∈ Z with xi = 1. We reduce the problem to determine g(d, k) 6 to a combinatorial problem related to the generalized k-girth of a graph G which 7 is defined as the minimum order of an induced subgraph of G of m...

Our objective was to explore the relationships between adult attachment and various aspects of emotional awareness, including alexithymia and level of emotional awareness. Participants were 112 university students who completed the Attachment Style Questionnaire, the Bermond-Vorst Alexithymia Questionnaire (BVAQ), and the Level of Emotional Awareness Scale. We found that alexithymia was positiv...