Related papers: Induced Matching below Guarantees: Average Paves t…
We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…
Let $G$ be a connected planar (but not yet embedded) graph and $F$ a set of additional edges not yet in $G$. The {multiple edge insertion} problem (MEI) asks for a drawing of $G+F$ with the minimum number of pairwise edge crossings, such…
We consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. In this problem, we are given an undirected graph. Each edge is assigned a known, independent probability of existence and…
Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples of such problems include maximum independent set, maximum planar graph, and many others. We…
In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs $G_1$ and $G_2$, one looks for a graph with the maximum number of vertices being both an induced subgraph of $G_1$ and $G_2$. MCIS is among the most studied…
In the Fully Leafed Induced Subtrees, one is given a graph $G$ and two integers $a$ and $b$ and the question is to find an induced subtree of $G$ with $a$ vertices and at least $b$ leaves. This problem is known to be NP-complete even when…
In the total matching problem, one is given a graph $G$ with weights on the vertices and edges. The goal is to find a maximum weight set of vertices and edges that is the non-incident union of a stable set and a matching. We consider the…
A graph $G$ contains a graph $H$ as an induced minor if $H$ can be obtained from $G$ by vertex deletions and edge contractions. The class of $H$-induced-minor-free graphs generalizes the class of $H$-minor-free graphs, but unlike…
In the stochastic matching problem, we are given a general (not necessarily bipartite) graph $G(V,E)$, where each edge in $E$ is realized with some constant probability $p > 0$ and the goal is to compute a bounded-degree (bounded by a…
We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are interested in the parameter Ie(G), which, for a given graph…
We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an $\ell$-matchoid $\cm$ on a ground set $E$, a profit function $p:E \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:E \rightarrow…
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal…
For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research.…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. Finding an…
We prove that finding a $k$-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai. Our algorithm is based on several combinatorial observations, Gauss' famous \emph{Eureka} theorem [Andrews,…
A \emph{matching} is a subset of edges in a graph $G$ that do not share an endpoint. A matching $M$ is a \emph{$\mathcal{P}$-matching} if the subgraph of $G$ induced by the endpoints of the edges of $M$ satisfies property $\mathcal{P}$. For…
We show that if $G$ is a connected graph of maximum degree at most $4$, which is not $C_{2,5}$, then the strong matching number of $G$ is at least $\frac{1}{9}n(G)$. This bound is tight and the proof implies a polynomial time algorithm to…
Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be…