Abstract. A real n × n matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k × k principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are...

The upward planarity testing problem consists of testing if a digraph admits a drawing Γ such that all edges in Γ are monotonically increasing in the vertical direction and no edges in Γ cross. In this paper we reduce the problem of testing a digraph for upward planarity to the problem of testing if its blocks admit upward planar drawings with certain properties. We also show how to test if a b...

A vertex set X of a digraph D = (V, A) is a kernel if X is independent (i.e., all pairs of distinct vertices of X are non-adjacent) and for every v ∈ V − X there exists x ∈ X such that vx ∈ A. A vertex set X of a digraph D = (V, A) is a quasi-kernel if X is independent and for every v ∈ V − X there exist w ∈ V − X, x ∈ X such that either vx ∈ A or vw, wx ∈ A. In 1994, Chvátal and Lovász proved ...

In this article, we present a detailed study of the reach distance-layer structure De Bruijn and Kautz digraphs, apply our analysis to performance evaluation deflection routing in networks. Concerning structure, provide explicit polynomial expressions, terms degree digraph, for cardinalities some relevant sets structure. Regarding application defection routing, as consequence description formul...

For a digraph D, let λ(D) be the arc-strong-connectivity of D. For an integer k > 0, a simple digraph Dwith |V (D)| ≥ k + 1 is k-maximal if every subdigraph H of D satisfies λ(H) ≤ k but for adding new arc to D results in a subdigraph H ′ with λ(H ) ≥ k + 1. We prove that if D is a simple k-maximal digraph on n > k + 1 ≥ 2 vertices, then |A(D)| ≥ n 2  + (n − 1)k +  n k + 2   1 + 2k −  k +...

Given a digraph D, let δ(D) := min{δ(D), δ−(D)} be the minimum degree of D. We show that every sufficiently large digraph D with δ(D) ≥ n/2 + l − 1 is l-linked. The bound on the minimum degree is best possible and confirms a conjecture of Manoussakis [16]. We also determine the smallest minimum degree which ensures that a sufficiently large digraph D is k-ordered, i.e. that for every sequence s...

The main concern of this article is to present and motivate the Rubis method for tackling the choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative. Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. Th...

A semicomplete multipartite or semicomplete c-partite digraph D is a biorientation of a c-partite graph. A semicomplete multipartite digraph D is called strongly quasiHamiltonian-connected, if for any two distinct vertices x and y of D, there is a path P from x to y such that P contains at least one vertex from each partite set of D. In this paper we show that every 4-strong semicomplete multip...

An n-lift of a digraph K, is a digraph with vertex set V (K)× [n] and for each directed edge (i, j) ∈ E(K) there is a perfect matching between fibers {i} × [n] and {j} × [n], with edges directed from fiber i to fiber j. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that if h is sufficiently large then a random n-lift of the...

Suppose that D = (V,E) is a strongly connected digraph. Let u, v ∈ V (D). The maximum distance md(u, v) is defined as md(u, v)=max{ −→ d (u, v), −→ d (v, u)} where −→ d (u, v) denote the length of a shortest directed u− v path in D. This is a metric. The boundary, contour, eccentric and peripheral sets of a strong digraph D are defined with respect to this metric. The main aim of this paper is ...