Related papers: Minimal strong digraphs

A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of…

This paper has two parts. In the first one, we prove that an invariant dp-minimal type is either finitely satisfiable or definable. We also prove that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium…

Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…

Chordal graphs are important in algorithmic graph theory. Chordal digraphs are a digraph analogue of chordal graphs and have been a subject of active studies recently. Unlike chordal graphs, chordal digraphs lack many structural properties…

The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…

We analyse an extremal question on the degrees of the link graphs of a finite regular graph, that is, the subgraphs induced by non-trivial spheres. We show that if $G$ is $d$-regular and connected but not complete then some link graph of…

For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant…

Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and…

A graph G is said to be 2-distinguishable if there is a 2-labeling of its vertices which is not preserved by any nontrivial automorphism of G. We show that every locally finite graph with infinite motion and growth at most…

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…

The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification…

Let $D$ be an directed graph on $p\geq 10$ vertices with minimum degree at least $p-1$ and minimum semi-degree at least $ p/2 -1$. We present a detailed proof of the following result [13]: The digraph $D$ is pancyclic, unless some extremal…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

A digraph is connected-homogeneous if every isomorphism between two finite connected induced subdigraphs extends to an automorphism of the whole digraph. In this paper, we completely classify the countable connected-homogeneous digraphs.

We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…

A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…

Strong product is an efficient way to construct a larger digraph through some specific small digraphs. The large digraph constructed by the strong product method contains the factor digraphs as its subgraphs, and can retain some good…

Let $G$ be a digraph and $r(G)$ be its rank. Many interesting results on the rank of an undirected graph appear in the literature, but not much information about the rank of a digraph is available. In this article, we study the rank of a…

Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…