Related papers: Simultaneous Interval Graphs
We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…
Given an elementary chain of vertex set V, seen as a labelling of V by the set {1, ...,n=|V|}, and another discrete structure over $V$, say a graph G, the problem of common intervals is to compute the induced subgraphs G[I], such that $I$…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration,…
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…
We consider two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities p_1,p_2. In particular, (i) we prove a sharp threshold result for the appearance of G_{n,p_1}…
In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval…
Let $G=(V_1(G),V_2(G),E(G))$ be a bipartite multigraph, and $R\subseteq V_1(G)\cup V_2(G)$. A proper coloring of edges of $G$ with the colors $1,\ldots,t$ is called interval (respectively, continuous) on $R$, if each color is used for at…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two…
We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
A seminal result by Whitney describes when two graphs have the same cycles. We consider the analogous problem for even cycle matroids. A representation of an even cycle matroid is a pair formed by a graph together with a special set of…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
An induced matching $M$ in a graph $G$ is dominating if every edge not in $M$ shares exactly one vertex with an edge in $M$. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph $G$ contains…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
A \emph{mixed interval graph} is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are…