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Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a…
In the paper we consider the problem of scheduling $n$ identical jobs on 3 uniform machines with speeds $s_1, s_2,$ and $s_3$ to minimize the schedule length. We assume that jobs are subjected to some kind of mutual exclusion constraints,…
Graphs are widely used to encapsulate a variety of data formats, but real-world networks often involve complex node relations beyond only being pairwise. While hypergraphs and hierarchical graphs have been developed and employed to account…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. The word-representability of split graphs was studied in a series of papers in the literature, and the class of word-representable split…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
In recent years, Dynamic Graph (DG) representations have been increasingly used for modeling dynamic systems due to their ability to integrate both topological and temporal information in a compact representation. Dynamic graphs allow to…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
A maximal matching $M$ that consists of independent edges is a subgraph of a simple and undirected graph $G$ for which $G-M$ forms an independent set. A graph $G$ is called equimatchable if all maximal matchings have the same number of…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
(Induced) Subgraph Isomorphism and Maximum Common (Induced) Subgraph are fundamental problems in graph pattern matching and similarity computation. In graphs derived from time-series data or protein structures, a natural total ordering of…
Visibility problems have been investigated for a long time under different assumptions as they pose challenging combinatorial problems and are connected to robot navigation problems. The mutual-visibility problem in a graph $G$ of $n$…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether…
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…
We study the recognition complexity of subgraphs of k-connected planar cubic graphs for k = 1, 2, 3. We present polynomial-time algorithms to recognize subgraphs of 1- and 2-connected planar cubic graphs, both in the variable and fixed…