4 citations · 16 across the 22 of their papers we have counts for
7 papers · 1 filter
On the Complexity of Vertex-Splitting Into an Interval Graph
Faisal N. Abu-Khzam, Dipayan Chakraborty, Lucas Isenmann +1
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the orig…
On the Complexity of Claw-Free Vertex Splitting
Faisal N. Abu-Khzam, Sergio Thoumi
Vertex splitting consists of taking a vertex in a graph and replacing it with two non-adjacent vertices whose combined neighborhoods is the neighborhood of . The split is sa…
Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter
Faisal N. Abu-Khzam, Lucas Isenmann
The s-club cluster vertex deletion number of a graph, or sccvd, is the minimum number of vertices whose deletion results in a disjoint union of s-clubs, or graphs whose diameter is…
Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes
Faisal N. Abu-Khzam, Henning Fernau, Kevin Mann
The concept of Roman domination has recently been studied concerning enumerating and counting (WG 2022). It has been shown that minimal Roman dominating functions can be enumerated…
Enumerating Connected Dominating Sets
Faisal Abu-Khzam, Henning Fernau, Benjamin Gras +2
The question to enumerate all inclusion-minimal connected dominating sets in a graph of order in time significantly less than is an open question that was asked in many p…
Cluster Editing with Vertex Splitting
Faisal N. Abu-Khzam, Emmanuel Arrighi, Matthias Bentert +7
Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to edge…
Partitioning a Graph into Disjoint Cliques and a Triangle-free Graph
Faisal N. Abu-Khzam, Carl Feghali, Haiko Müller
A graph is \emph{partitionable} if there exists a partition of such that induces a disjoint union of cliques and induces a triangle-free graph.…