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This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
Genome assembly is a fundamental problem in Bioinformatics, where for a given set of overlapping substrings of a genome, the aim is to reconstruct the source genome. The classical approaches to solving this problem use assembly graphs, such…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where N[v] is the closed neighbourhood of v.…
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect H-packings: Given positive integers n, r, D, we…
Let integers $r\ge 2$ and $d\ge 3$ be fixed. Let ${\cal G}_d$ be the set of graphs with no induced path on $d$ vertices. We study the problem of packing $k$ vertex-disjoint copies of $K_{1,r}$ ($k\ge 2$) into a graph $G$ from parameterized…
We give the first linear kernels for the (Connected) Dominating Set problems on H-topological minor free graphs. We prove the existence of polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer…
We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed $\alpha$ between zero and one we are given a graph and two numbers $k \in \mathbb{N}$ and $t \in \mathbb{Q}$. The…
Graph separation and partitioning are fundamental problems that have been extensively studied both in theory and practice. The \textsc{$p$-Size Separator} problem, closely related to the \textsc{Balanced Separator} problem, is to check…
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the…
Given an undirected graph $G = (V_G, E_G)$ and a fixed "pattern" graph $H = (V_H, E_H)$ with $k$ vertices, we consider the $H$-Transversal and $H$-Packing problems. The former asks to find the smallest $S \subseteq V_G$ such that the…
Given two graphs $G$ and $H$, we define $\textsf{v-cover}_{H}(G)$ (resp. $\textsf{e-cover}_{H}(G)$) as the minimum number of vertices (resp. edges) whose removal from $G$ produces a graph without any minor isomorphic to ${H}$. Also…
Cohesive subgraph discovery in a network is one of the fundamental problems and investigated for several decades. In this paper, we propose the Overlapping Cohesive Subgraphs with Minimum degree (OCSM) problem which combines three key…
Clustering a graph when the clusters can overlap can be seen from three different angles: We may look for cliques that cover the edges of the graph with bounded overlap, we may look to add or delete few edges to uncover the cluster…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Finding large "cliquish" subgraphs is a classic NP-hard graph problem. In this work, we focus on finding maximum $s$-clubs and $s$-plexes, i.e., graphs of diameter $s$ and graphs where each vertex is adjacent to all but $s$ vertices.…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…