
Independent sets in (P_4+P_4,Triangle)free graphs
The Maximum Weight Independent Set Problem (WIS) is a wellknown NPhard...
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Computing metric hulls in graphs
We prove that, given a closure function the smallest preimage of a close...
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Maximum Weight Independent Sets for (S_1,2,4,Triangle)Free Graphs in Polynomial Time
The Maximum Weight Independent Set (MWIS) problem on finite undirected g...
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Temporal Reachability Minimization: Delaying vs. Deleting
We study spreading processes in temporal graphs, i. e., graphs whose con...
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Robustness: a New Form of Heredity Motivated by Dynamic Networks
We investigate a special case of hereditary property in graphs, referred...
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Solving Partition Problems Almost Always Requires Pushing Many Vertices Around
A fundamental graph problem is to recognize whether the vertex set of a ...
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Fair packing of independent sets
In this work we add a graph theoretical perspective to a classical probl...
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On the monophonic rank of a graph
A set of vertices S of a graph G is monophonically convex if every induced path joining two vertices of S is contained in S. The monophonic convex hull of S, ⟨ S ⟩, is the smallest monophonically convex set containing S. A set S is monophonic convexly independent if v ∉⟨ S  {v}⟩ for every v ∈ S. The monophonic rank of G is the size of the largest monophonic convexly independent set of G. We present a characterization of the monophonic convexly independent sets. Using this result, we show how to determine the monophonic rank of graph classes like bipartite, cactus, trianglefree, and line graphs in polynomial time. Furthermore, we show that this parameter can computed in polynomial time for 1starlike graphs, i.e., for split graphs, and that its determination is complete for kstarlike graphs for any fixed k ≥ 2, a subclass of chordal graphs. We also consider this problem on the graphs whose intersection graph of the maximal prime subgraphs is a tree.
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