Related papers: Linear rank-width of distance-hereditary graphs I.…
We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…
It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show…
The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…
In this paper we consider the directed path-width and directed tree-width of recursively defined digraphs. As an important combinatorial tool, we show how the directed path-width and the directed tree-width can be computed for the disjoint…
We consider the problem of inferring an edge-labeled graph from the sequence of edge labels seen in a walk of that graph. It has been known that this problem is solvable in $O(n \log n)$ time when the targets are path or cycle graphs. This…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary…
We propose an algorithm whose input are parameters $k$ and $r$ and a hypergraph $H$ of rank at most $r$. The algorithm either returns a tree decomposition of $H$ of generalized hypertree width at most $4k$ or 'NO'. In the latter case, it is…
Given an undirected weighted graph, an (approximate) distance oracle is a data structure that can (approximately) answer distance queries. A {\em Path-Reporting Distance Oracle}, or {\em PRDO}, is a distance oracle that must also return a…
We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently:…
We study the classic problem of subgraph counting, where we wish to determine the number of occurrences of a fixed pattern graph $H$ in an input graph $G$ of $n$ vertices. Our focus is on bounded degeneracy inputs, a rich family of graph…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
In the \textsc{Waypoint Routing Problem} one is given an undirected capacitated and weighted graph $G$, a source-destination pair $s,t\in V(G)$ and a set $W\subseteq V(G)$, of \emph{waypoints}. The task is to find a walk which starts at the…
A phylogenetic network is a graph-theoretical tool that is used by biologists to represent the evolutionary history of a collection of species. One potential way of constructing such networks is via a distance-based approach, where one is…
The concept of mutual-visibility in graphs has been recently introduced. If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,…
The following theorem is proved: For all $k$-connected graphs $G$ and $H$ each with at least $n$ vertices, the treewidth of the cartesian product of $G$ and $H$ is at least $k(n -2k+2)-1$. For $n\gg k$ this lower bound is asymptotically…
Computing the directed path-width of a directed graph is an NP-hard problem. Even for digraphs of maximum semi-degree 3 the problem remains hard. We propose a decomposition of an input digraph G=(V,A) by a number k of sequences with entries…
Given a linear ordering of the vertices of a graph, the cutwidth of a vertex $v$ with respect to this ordering is the number of edges from any vertex before $v$ (including $v$) to any vertex after $v$ in this ordering. The cutwidth of an…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
The study of structural graph width parameters like tree-width, clique-width and rank-width has been ongoing during the last five decades, and their algorithmic use has also been increasing [Cygan et al., 2015]. New width parameters…