Related papers: The Complexity of Maximum $k$-Order Bounded Compon…

Let $G = (V,E)$ be a simple, undirected and connected graph. A connected dominating set $S \subseteq V$ is a secure connected dominating set of $G$, if for each $ u \in V\setminus S$, there exists $v\in S$ such that $(u,v) \in E$ and the…

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

Enumerating maximal $k$-biplexes (MBPs) of a bipartite graph has been used for applications such as fraud detection. Nevertheless, there usually exists an exponential number of MBPs, which brings up two issues when enumerating MBPs, namely…

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…

A set $S\subseteq V$ of a graph $G=(V,E)$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Dominating Set is the problem of deciding, given a graph $G$ and an integer $k\geq 1$, if $G$ has a dominating set of size…

In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…

The induced odd cycle packing number $iocp(G)$ of a graph $G$ is the maximum integer $k$ such that $G$ contains an induced subgraph consisting of $k$ pairwise vertex-disjoint odd cycles. Motivated by applications to geometric graphs, Bonamy…

We consider the classic budgeted maximum weight independent set (BMWIS) problem. The input is a graph $G = (V,E)$, a weight function $w:V \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:V \rightarrow \mathbb{R}_{\geq 0}$, and a budget…

Given a positive integer $k$, a $k$-dominating set in a graph $G$ is a set of vertices such that every vertex not in the set has at least $k$ neighbors in the set. A total $k$-dominating set, also known as a $k$-tuple total dominating set,…

Let $\mathcal{G}$ be a minor-closed graph class. We say that a graph $G$ is a $k$-apex of $\mathcal{G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to $\mathcal{G}.$ We denote by $\mathcal{A}_k…

Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…

We present a 6-approximation algorithm for the minimum-cost $k$-node connected spanning subgraph problem, assuming that the number of nodes is at least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the Frank-Tardos…

An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…

We study the inapproximability of the induced disjoint paths problem on an arbitrary $n$-node $m$-edge undirected graph, which is to connect the maximum number of the $k$ source-sink pairs given in the graph via induced disjoint paths. It…

For a graph $G$, a vertex subset $S$ is called a maximum generalized $k$-independent set if the induced subgraph $G[S]$ does not contain a $k$-tree as its subgraph, and the subset has maximum cardinality. The generalized $k$-independence…

We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…

In a graph $G = (V,E)$, a k-ruling set $S$ is one in which all vertices $V$ \ $S$ are at most $k$ distance from $S$. Finding a minimum k-ruling set is intrinsically linked to the minimum dominating set problem and maximal independent set…

We consider the \emph{Budgeted} version of the classical \emph{Connected Dominating Set} problem (BCDS). Given a graph $G$ and a budget $k$, we seek a connected subset of at most $k$ vertices maximizing the number of dominated vertices in…

Given a graph $G=(V,E)$, for a vertex set $S\subseteq V$, let $N(S)$ denote the set of vertices in $V$ that have a neighbor in $S$. Extending the concept of binding number of graphs by Woodall~(1973), for a vertex set $X \subseteq V$, we…

A graph $U$ is an induced universal graph for a family $F$ of graphs if every graph in $F$ is a vertex-induced subgraph of $U$. For the family of all undirected graphs on $n$ vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an…