
Feedback Vertex Set on Hamiltonian Graphs
We study the computational complexity of Feedback Vertex Set on subclass...
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3Coloring on Regular, Planar, and Ordered Hamiltonian Graphs
We prove that 3Coloring remains NPhard on 4 and 5regular planar Hami...
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Computational Complexity of Three Central Problems in Itemset Mining
Itemset mining is one of the most studied tasks in knowledge discovery. ...
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On Computing the Hamiltonian Index of Graphs
The rth iterated line graph L^r(G) of a graph G is defined by: (i) L^0(...
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CPG graphs: Some structural and hardness results
In this paper we continue the systematic study of Contact graphs of Path...
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Generation of random chordal graphs using subtrees of a tree
Chordal graphs form one of the most studied graph classes. Several graph...
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Complexity continuum within Ising formulation of NP problems
A promising approach to achieve computational supremacy over the classic...
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Most Classic Problems Remain NPhard on Relative Neighborhood Graphs and their Relatives
Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs mostly remained open. We now study 3Colorability, Dominating Set, Feedback Vertex Set, Hamiltonian Cycle, and Independent Set on the proximity graph classes relative neighborhood graphs, Gabriel graphs, and relatively closest graphs. We prove that all of the problems remain NPhard on these graphs, except for 3Colorability and Hamiltonian Cycle on relatively closest graphs, where the former is trivial and the latter is left open. Moreover, for every NPhard case we additionally show that no 2^o(n^1/4)time algorithm exists unless the ETH fails, where n denotes the number of vertices.
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