Related papers: Gerrymandering on graphs: Computational complexity…
The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
A dominating set of a graph is a set of vertices such that every vertex not in the set has at least one neighbor in the set. The problem of counting dominating sets is #P-complete for chordal graphs but solvable in polynomial time for its…
We consider a generalized poset sorting problem (GPS), in which we are given a query graph $G = (V, E)$ and an unknown poset $\mathcal{P}(V, \prec)$ that is defined on the same vertex set $V$, and the goal is to make as few queries as…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex…
For a graph class $\mathcal{G}$, we define the $\mathcal{G}$-modular cardinality of a graph $G$ as the minimum size of a vertex partition of $G$ into modules that each induces a graph in $\mathcal{G}$. This generalizes other module-based…
In a graph $G$, a vertex subset $S\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of a graph $G$ is called a paired-dominating set if the induced subgraph…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…
Given a graph $G = (V, E)$ and an integer $k$, the Minimum Membership Dominating Set problem asks to compute a set $S \subseteq V$ such that for each $v \in V$, $1 \leq |N[v] \cap S| \leq k$. The problem is known to be NP-complete even on…
In this paper, we study two popular variants of Graph Coloring -- Dominator Coloring and CD Coloring. In both problems, we are given a graph $G$ and a natural number $\ell$ as input and the goal is to properly color the vertices with at…
$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…