Related papers: A characterization of interval nest digraphs
We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…
Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of subpaths of a path. Since cycles are locally paths, every…
We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard…
The interval number of a graph $G$ is the minimum $k$ such that one can assign to each vertex of $G$ a union of $k$ intervals on the real line, such that $G$ is the intersection graph of these sets, i.e., two vertices are adjacent in $G$ if…
A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the…
The stress interval $S(u,v)$ between $u,v\in V(G)$ is the set of all vertices in a graph $G$ that lie on every shortest $u,v$-path. A set $U \subseteq V(G)$ is stress convex if $S(u,v) \subseteq U$ for any $u,v\in U$. A vertex $v \in V(G)$…
For two strings u, v over some alphabet A, we investigate the problem of embedding u into w as a subsequence under the presence of generalised gap constraints. A generalised gap constraint is a triple (i, j, C_{i, j}), where 1 <= i < j <=…
If the vertices composing a network interact at distinct time points, the temporal ordering of these interactions and the network's graph structure are sufficient to convey the routes by which information can flow in the network. Two…
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 introduce and study the pinnacle sets of a simple graph $G$ with $n$ vertices. Given a bijective vertex labeling $\lambda\,:\,V(G)\rightarrow [n]$, the label $\lambda(v)$ of vertex $v$ is a pinnacle of $(G, \lambda)$ if…
Let $W(G)$ be the Wiener index of a graph $G$. We say that a vertex $v \in V(G)$ is a \v{S}olt\'es vertex in $G$ if $W(G - v) = W(G)$, i.e. the Wiener index does not change if the vertex $v$ is removed. In 1991, \v{S}olt\'es posed the…
Grammar inference deals with determining (preferable simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly…
An automata network with $n$ components over a finite alphabet $Q$ of size $q$ is a discrete dynamical system described by the successive iterations of a function $f:Q^n\to Q^n$. In most applications, the main parameter is the interaction…
A nut graph is a singular graph with one-dimensional kernel and corresponding eigenverctor with no zero elements. The problem of determining the orders $n$ for which $d$-regular nut graphs exist was recently posed by Gauci, Pisanski and…
A tangled-diagram over $[n]=\{1,...,n\}$ is a graph of degree less than two whose vertices $1,...,n$ are arranged in a horizontal line and whose arcs are drawn in the upper halfplane with a particular notion of crossings and nestings.…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
In this paper, we consider a variant of dichromatic number on digraphs with prescribed sets of arcs. Let $D$ be a digraph and let $Z_1, Z_2$ be two sets of arcs in $D$. For a subdigraph $H$ of $D$, let $A(H)$ denote the set of all arcs of…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A family $\mathcal{S}$ of nonempty sets $\{S_1,\ldots,S_n\}$ is a set representation of $G$ if there exists a one-to-one correspondence between the vertices $v_1, \ldots, v_n$…
An acyclic digraph in which every vertex has indegree at most $i$ and outdegree at most $j$ is called an $(i,j)$ digraph for some positive integers $i$ and $j$. The phylogeny graph of a digraph $D$ has $V(D)$ as the vertex set and an edge…
It has been known since 1991 that the problem of recognizing grid intersection graphs is NP-complete. Here we use a modified argument of the above result to show that even if we restrict to the class of unit grid intersection graphs…