Related papers: Token Sliding on Chordal Graphs

We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of…

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\geq 1, the task is to decide whether G contains a set S\subseteq V(G)…

We study the problem of reconfiguring one minimum $s$-$t$-separator $A$ into another minimum $s$-$t$-separator $B$ in some $n$-vertex graph $G$ containing two non-adjacent vertices $s$ and $t$. We consider several variants of the problem as…

We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…

We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…

In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…

Given a graph $G$ with a terminal set $R \subseteq V(G)$, the Steiner tree problem (STREE) asks for a set $S\subseteq V(G) \setminus R$ such that the graph induced on $S\cup R$ is connected. A split graph is a graph which can be partitioned…

Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…

The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and…

We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph $G=(V,E)$ and a vertex set $U \subseteq V$, it is asked if there exists a minimal vertex cover (resp.\ maximal independent set)…

A bipartite graph is chordal bipartite if every cycle of length at least 6 has a chord in it. In this paper, we investigate the structure of $P_5$-free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering,…

We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…

We consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a…

A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\alpha(G[N(v_{i})\cap V_{i}])\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\{v_{i},...,v_{n}\}$ and $\alpha$…

Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\in E(G)$ are said to have a \emph{common edge} $e\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an…

We present an algorithm that takes as input a graph $G$ with weights on the vertices, and computes a maximum weight independent set $S$ of $G$. If the input graph $G$ excludes a path $P_k$ on $k$ vertices as an induced subgraph, the…

A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The decision problem whether a graph has a disconnected cut is called Disconnected Cut. This problem is closely related to several…

The problems of Permutation Routing via Matching and Token Swapping are reconfiguration problems on graphs. This paper is concerned with the complexity of those problems and a colored variant. For a given graph where each vertex has a…

Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In…