
Tractability of Konig Edge Deletion Problems
A graph is said to be a Konig graph if the size of its maximum matching ...
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Parameterized Orientable Deletion
A graph is dorientable if its edges can be oriented so that the maximum...
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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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Deleting edges to restrict the size of an epidemic in temporal networks
A variety of potentially diseasespreading contact networks can be natur...
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The Complexity of Connectivity Problems in ForbiddenTransition Graphs and EdgeColored Graphs
The notion of forbiddentransition graphs allows for a robust generaliza...
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Width Parameterizations for Knotfree Vertex Deletion on Digraphs
A knot in a directed graph G is a strongly connected subgraph Q of G wit...
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Structural Parameterizations of Tracking Paths Problem
Given a graph G with source and destination vertices s,t∈ V(G) respectiv...
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Edge Deletion to Restrict the Size of an Epidemic
Given a graph G=(V,E), a set ℱ of forbidden subgraphs, we study ℱFree Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any F∈ℱ as a subgraph. For the parameter treewidth, the question of whether the problem is FPT has remained open. Here we give a negative answer by showing that the problem is W[1]hard when parameterized by the treewidth, which rules out FPT algorithms under common assumption. Thus we give a solution to the conjecture posted by Jessica Enright and Kitty Meeks in [Algorithmica 80 (2018) 18571889]. We also prove that the ℱFree Edge Deletion problem is W[2]hard when parameterized by the solution size k, feedback vertex set number or pathwidth of the input graph. A special case of particular interest is the situation in which ℱ is the set 𝒯_h+1 of all trees on h+1 vertices, so that we delete edges in order to obtain a graph in which every component contains at most h vertices. This is desirable from the point of view of restricting the spread of disease in transmission network. We prove that the 𝒯_h+1Free Edge Deletion problem is fixedparameter tractable (FPT) when parameterized by the vertex cover number. We also prove that it admits a kernel with O(hk) vertices and O(h^2k) edges, when parameterized by combined parameters h and the solution size k.
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