Related papers: $\mathcal{P}$-matchings Parameterized by Treewidth
Enumerating the minimal hitting sets of a hypergraph is a problem which arises in many data management applications that include constraint mining, discovering unique column combinations, and enumerating database repairs. Previously, Eiter…
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…
A \emph{wheel} is a graph made of a cycle of length at least~4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph $G$ and whose question is "does $G$ contains a wheel…
We contribute to the sparsely populated area of unsupervised deep graph matching with application to keypoint matching in images. Contrary to the standard \emph{supervised} approach, our method does not require ground truth correspondences…
A metric space $\mathcal{T}$ is a \emph{real tree} if for any pair of points $x, y \in \mathcal{T}$ all topological embeddings $\sigma$ of the segment $[0,1]$ into $\mathcal{T}$, such that $\sigma (0)=x$ and $\sigma (1)=y$, have the same…
The metric dimension has been introduced independently by Harary, Melter and Slater in 1975 to identify vertices of a graph G using its distances to a subset of vertices of G. A resolving set X of a graph G is a subset of vertices such…
Two strings $x$ and $y$ over $\Sigma \cup \Pi$ of equal length are said to \emph{parameterized match} (\emph{p-match}) if there is a renaming bijection $f:\Sigma \cup \Pi \rightarrow \Sigma \cup \Pi$ that is identity on $\Sigma$ and…
The matching number of a graph G is the size of a maximum matching in the graph. In this note, we present a sufficient condition involving the matching number for the Hamiltonicity of graphs.
We present fixed parameter tractable algorithms for the conflict-free coloring problem on graphs. Given a graph $G=(V,E)$, \emph{conflict-free coloring} of $G$ refers to coloring a subset of $V$ such that for every vertex $v$, there is a…
Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…
A \emph{2-interval} is the union of two disjoint intervals on the real line. Two 2-intervals $D_1$ and $D_2$ are \emph{disjoint} if their intersection is empty (i.e., no interval of $D_1$ intersects any interval of $D_2$). There can be…
Two plane drawings of graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. Let $S$ be a convex point set of $2n \geq 10$ points and let $\mathcal{H}$ be a family of…
We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…
The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph, which is proposed first by Gutman and Wagner [The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177--2187].…
In a graph, a (perfect) matching cut is an edge cut that is a (perfect) matching. Matching Cut (MC), respectively, Perfect Matching Cut (PMC), is the problem of deciding whether a given graph has a matching cut, respectively, a perfect…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
The goal of this work is to give precise bounds on the counting complexity of a family of generalized coloring problems (list homomorphisms) on bounded-treewidth graphs. Given graphs $G$, $H$, and lists $L(v)\subseteq V(H)$ for every $v\in…