Related papers: Independent Set Reconfiguration Under Bounded-Hop …
Given two independent sets $I, J$ of a graph $G$, and imagine that a token (coin) is placed at each vertex of $I$. The Sliding Token problem asks if one could transform $I$ to $J$ via a sequence of elementary steps, where each step requires…
We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…
Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In…
We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of…
Reconfiguration problems involve determining whether two given configurations can be transformed into each other under specific rules. The Token Sliding problem asks whether, given two different set of tokens on vertices of a graph $G$, we…
Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified…
Let $G=(V,E)$ and $H$ be two graphs. Packing problem is to find in $G$ the largest number of independent subgraphs each of which is isomorphic to $H$. Let $U\subset{V}$. If the graph $G-U$ has no subgraph isomorphic to $H$, $U$ is a cover…
This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…
In a reconfiguration version of an optimization problem $\mathcal{Q}$ the input is an instance of $\mathcal{Q}$ and two feasible solutions $S$ and $T$. The objective is to determine whether there exists a step-by-step transformation between…
The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical…
The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RH\Pi_1. It is believed that #BIS does not have an…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the…
Given a graph $G = (V,E)$, a set $T$ of vertex pairs, and an integer $k$, Hitting Geodesic Intervals asks whether there is a set $S \subseteq V$ of size at most $k$ such that for each terminal pair $\{u,v\} \in T$, the set $S$ intersects at…
We study the parameterized complexity of a variant of the $F$-free Editing problem: Given a graph $G$ and a natural number $k$, is it possible to modify at most $k$ edges in $G$ so that the resulting graph contains no induced subgraph…
An irreversible $k$-threshold process (also a $k$-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least $k$ black neighbors. An irreversible $k$-conversion set…
We consider the following problem closely related to graph isomorphism. In a simplified version, the task is to compute the automorphism group of a given set family (or a hypergraph), that is, the group of all automorphisms of the given…
A vertex-subset graph problem $Q$ defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem $Q$ asks whether it is possible to transform one feasible solution for…
Repair operators are often used for constraint handling in constrained combinatorial optimization. We investigate the (1+1)~EA equipped with a tailored jump-and-repair operation that can be used to probabilistically repair infeasible…
A $k$-path vertex cover ($k$-PVC) of a graph $G$ is a vertex subset $I$ such that each path on $k$ vertices in $G$ contains at least one member of $I$. Imagine that a token is placed on each vertex of a $k$-PVC. Given two $k$-PVCs $I, J$ of…