
A lineartime algorithm for semitotal domination in strongly chordal graphs
In a graph G=(V,E) with no isolated vertex, a dominating set D ⊆ V, is c...
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Twinwidth and polynomial kernels
We study the existence of polynomial kernels, for parameterized problems...
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On the complexity of Broadcast Domination and Multipacking in digraphs
We study the complexity of the two dual covering and packing distanceba...
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The Dominating Set Problem in Geometric Intersection Graphs
We study the parameterized complexity of dominating sets in geometric in...
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Solving problems on generalized convex graphs via mimwidth
A bipartite graph G=(A,B,E) is Hconvex, for some family of graphs H, if...
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Dominating sets reconfiguration under token sliding
Let G be a graph and D_s and D_t be two dominating sets of G of size k. ...
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Budgeted Dominating Sets in Uncertain Graphs
We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, ...
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Semitotal Domination: New hardness results and a polynomialtime algorithm for graphs of bounded mimwidth
A semitotal dominating set of a graph G with no isolated vertex is a dominating set D of G such that every vertex in D is within distance two of another vertex in D. The minimum size γ_t2(G) of a semitotal dominating set of G is squeezed between the domination number γ(G) and the total domination number γ_t(G). Semitotal Dominating Set is the problem of finding, given a graph G, a semitotal dominating set of G of size γ_t2(G). In this paper, we continue the systematic study on the computational complexity of this problem when restricted to special graph classes. In particular, we show that it is solvable in polynomial time for the class of graphs with bounded mimwidth by a reduction to Total Dominating Set and we provide several approximation lower bounds for subclasses of subcubic graphs. Moreover, we obtain complexity dichotomies in monogenic classes for the decision versions of Semitotal Dominating Set and Total Dominating Set. Finally, we show that it is NPcomplete to recognise the graphs such that γ_t2(G) = γ_t(G) and those such that γ(G) = γ_t2(G), even if restricted to be planar and with maximum degree at most 4, and we provide forbidden induced subgraph characterisations for the graphs heriditarily satisfying either of these two equalities.
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