
Defensive Alliances in Graphs
A set S of vertices of a graph is a defensive alliance if, for each elem...
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Multistage st Path: Confronting Similarity with Dissimilarity
Addressing a quest by Gupta et al. [ICALP'14], we provide a first, compr...
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On Minimum Connecting Transition Sets in Graphs
A forbidden transition graph is a graph defined together with a set of p...
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Spy game: FPTalgorithm, hardness and graph products
In the (s,d)spy game over a graph G, k guards and one spy occupy some v...
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Sharp bounds for the chromatic number of random Kneser graphs
Given positive integers n> 2k, a Kneser graph KG_n,k is a graph whose ve...
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On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal
Let vc(G), fvs(G) and oct(G), respectively, denote the size of a minimum...
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Computational Complexity of Covering Twovertex Multigraphs with Semiedges
We initiate the study of computational complexity of graph coverings, ak...
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Reducing graph transversals via edge contractions
For a graph parameter π, the Contraction(π) problem consists in, given a graph G and two positive integers k,d, deciding whether one can contract at most k edges of G to obtain a graph in which π has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where π is the size of a minimum dominating set. We focus on graph parameters defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection H according to a fixed containment relation. We prove coNPhardness results under some assumptions on the graphs in H, which in particular imply that Contraction(π) is coNPhard even for fixed k=d=1 when π is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.
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