Related papers: Exploring the Gap Between Treedepth and Vertex Cov…
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…
We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to…
Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the…
Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension…
Vertex Integrity is a graph measure which sits squarely between two more well-studied notions, namely vertex cover and tree-depth, and that has recently gained attention as a structural graph parameter. In this paper we investigate the…
The width measure \emph{treedepth}, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which---given as input…
The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian…
We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and…
Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…