A note on two comparability graphs
A prime factor theorem for a generalized direct product
We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.
A proof of some Schützenberger-type results for Eulerian paths and circuits on digraphs.
A Ramsey-Type Problem for Paths in Digraphs.
A remark on almost Moore digraphs of degree three.
A remark on isotopies of digraphs and permutation matrices
A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs.
A simple proof of the Aztec diamond theorem.
A Sokoban-type game and arc deletion within irregular digraphs of all sizes
Digraphs in which ordered pairs of out- and in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the endpoints of these intervals) are found in [1,5]. In this paper we construct, with help of Sokoban-type game, n-vertex irregular oriented graphs (irregular...
A sufficient condition for the existence of k-kernels in digraphs
In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with l(γ) ≢ 0 (mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has four short chords. Then D has a k-kernel. This result generalizes some previous results...
A survey of algebra of tournaments.
A tournament result deduced from harems.
A traceability conjecture for oriented graphs.
Acyclic digraphs and eigenvalues of -matrices.
Acyclic sets in -majority tournaments.
Additive decomposition of matrices under rank conditions and zero pattern constraints
This paper deals with additive decompositions of a given matrix , where the ranks of the summands are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
Algebraic approach to locally finite trees with one end
Let be an infinite locally finite tree. We say that has exactly one end, if in any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At...
Algorithmic aspects of bipartite graphs.
Alternating connectivity of digraphs
Alternating connectivity of tournaments