
Edge Deletion to Restrict the Size of an Epidemic
Given a graph G=(V,E), a set ℱ of forbidden subgraphs, we study ℱFree E...
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Parameterized complexity of edgecoloured and signed graph homomorphism problems
We study the complexity of graph modification problems for homomorphism...
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Interferencefree Walks in Time: Temporally Disjoint Paths
We investigate the computational complexity of finding temporally disjoi...
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Compatibility, embedding and regularization of nonlocal random walks on graphs
Several variants of the graph Laplacian have been introduced to model no...
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FixedTreewidthEfficient Algorithms for EdgeDeletion to Intersection Graph Classes
For a graph class 𝒞, the 𝒞EdgeDeletion problem asks for a given graph ...
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Waypoint Routing on Bounded Treewidth Graphs
In the Waypoint Routing Problem one is given an undirected capacitated a...
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LCS Graph Kernel Based on Wasserstein Distance in Longest Common Subsequence Metric Space
For graph classification tasks, many methods use a common strategy to ag...
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The Complexity of Connectivity Problems in ForbiddenTransition Graphs and EdgeColored Graphs
The notion of forbiddentransition graphs allows for a robust generalization of walks in graphs. In a forbiddentransition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbiddentransition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bioinformatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an indepth study of tractability with regards to various graphwidth parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbiddentransition graph is W[1]hard when parameterized by the vertexdeletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edgecolored graph; properly colored walks in edgecolored graphs is one of the most studied special cases of compatible walks in forbiddentransition graphs.
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