Related papers: Interval-Permutation Segment Graphs
Graph self-supervised learning (GSSL) has emerged as a compelling framework for extracting informative representations from graph-structured data without extensive reliance on labeled inputs. In this study, we introduce Graph Interplay…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
Interval graphs are intersection graphs of closed intervals of the real-line. The well-known computational problem, called recognition, asks whether an input graph $G$ can be represented by closed intervals, i.e., whether $G$ is an interval…
In this paper, we introduce the \emph{interval query problem} on cube-free median graphs. Let $G$ be a cube-free median graph and $\mathcal{S}$ be a commutative semigroup. For each vertex $v$ in $G$, we are given an element $p(v)$ in…
A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique- and rank-width of graphs, because it is one of the minimal hereditary classes of…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…
We present a new approach for learning unsupervised node representations in community graphs. We significantly extend the Interferometric Graph Transform (IGT) to community labeling: this non-linear operator iteratively extracts features…
We explore what could make recognition of particular intersection-defined classes hard. We focus mainly on unit grid intersection graphs (UGIGs), i.e., intersection graphs of unit-length axis-aligned segments and grid intersection graphs…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such…
We analyse properties of geometric intersection graphs to show the strict containment between some natural classes of geometric intersection graphs. In particular, we show the following properties: - A graph $G$ is outerplanar if and only…
Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
We obtain the scaling limits of random graphs drawn uniformly in three families of intersection graphs: permutation graphs, circle graphs, and unit interval graphs. The two first families typically generate dense graphs, in these cases we…
An interval graph is considered improper if and only if it has a representation such that an interval contains another interval. Previously these have been investigated in terms of balance and minimal forbidden interval subgraphs for the…