Related papers: Optimization over Degree Sequences of Graphs
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
In this paper, we investigate the problem of finding {\it bisections} (i.e., balanced bipartitions) in graphs. We prove the following two results for {\it all} graphs $G$: (1). $G$ has a bisection where each vertex $v$ has at least $(1/4 -…
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…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…
Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives. The problem is NP-complete in general, and consequently substantial…
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…
A graph $G$ is said to be an $(s, k)$-polar graph if its vertex set admits a partition $(A, B)$ such that $A$ and $B$ induce, respectively, a complete $s$-partite graph and the disjoint union of at most $k$ complete graphs. Polar graphs and…
It is known that the maximum cardinality cut problem is NP-hard even in chordal graphs. In this paper, we consider the time complexity of the problem in proper interval graphs, a subclass of chordal graphs, and propose a dynamic programming…
The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…
Finding dense subgraphs of a large network is a fundamental problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications over the last five decades. However, most existing…
We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring…
In the Roman domination problem, an undirected simple graph $G(V,E)$ is given. The objective of Roman domination problem is to find a function $f:V\rightarrow {\{0,1,2\}}$ such that for any vertex $v\in V$ with $f(v)=0$ must be adjacent to…
Let G be an undirected simple graph having n vertices and let f be a function defined to be f:V(G) -> {0,..., n-1}. An f-factor of G is a spanning subgraph H such that degree of a vertex v in H is f(v) for every vertex v in V(G). The…
We provide a deterministic polynomial-time algorithm that, for a given $k$-uniform hypergraph $H$ with $n$ vertices and edge density $d$, finds a complete $k$-partite subgraph of $H$ with parts of size at least ${c(d, k)(\log…
A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…