Related papers: Tight Running Time Lower Bounds for Vertex Deletio…
For a graph invariant $\pi$, the Contraction($\pi$) problem consists in, given a graph $G$ and two positive integers $k,d$, deciding whether one can contract at most $k$ edges of $G$ to obtain a graph in which $\pi$ has dropped by at least…
We investigate the computational complexity of edge-deletion and edge-contraction problems in fuzzy graphs. For any graph property {\Pi} that is hereditary under contractions (or deletions) and determined by 3-connected components, the…
For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. We prove that $H$-free Edge Deletion is NP-complete…
The $H$-Free Edge Deletion problem asks, for a given graph $G$ and an integer $k$, whether it is possible to delete at most $k$ edges from $G$ to make it $H$-free, that is, not containing $H$ as an induced subgraph. The $H$-Free Edge…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
We study $\tau$-Bounded-Density Edge Deletion ($\tau$-BDED), where given an undirected graph $G$, the task is to remove as few edges as possible to obtain a graph $G'$ where no subgraph of $G'$ has density more than $\tau$. The density of a…
Let G be an input graph with n vertices and m edges and let k be a fixed parameter. We provide a single exponential FPT algorithm with running time O(c^kn(n+m)), c= min {18,k} that turns graph G into an interval graph by deleting at most k…
We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations. Existing FPT algorithms for these problems…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
In a finite undirected graph $G=(V,E)$, a vertex $v \in V$ {\em dominates} itself and its neighbors in $G$. A vertex set $D \subseteq V$ is an {\em efficient dominating set} ({\em e.d.} for short) of $G$ if every $v \in V$ is dominated in…
We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the $2^{O(k^2)} n^{O(1)}$ time algorithm…
In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph $G=(V,E)$ and a specified, or "distinguished" vertex $p \in V$, MDD(min) is the problem of finding a minimum weight vertex set $S…
A graph class is hereditary if it is closed under vertex deletion. We give examples of NP-hard, PSPACE-complete and NEXPTIME-complete problems that become constant-time solvable for every hereditary graph class that is not equal to the…
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths…
We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and…
For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. $H$-free Edge Completion and $H$-free Edge Editing…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…
De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted treewidth resulting…