On the parameterized complexity of the geodesic hull number

Mamadou Moustapha Kanté,Thiago Marcilon,Rudini Sampaio

doi:10.1016/j.tcs.2019.05.005

On the parameterized complexity of the geodesic hull number

Mamadou Moustapha Kanté, Thiago Marcilon + Show 1 more

https://doi.org/10.1016/j.tcs.2019.05.005

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Journal: Theoretical Computer Science	Publication Date: May 20, 2019
Citations: 4

Affiliation: Laboratory of Computing, Modelling and Optimization of the Systems, French National Centre for Scientific Research, University of Clermont Auvergne, Universidade Federal do Cariri, Universidade Federal do Ceará

#Polynomial Time #Treewidth Tw + Show 3 more

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Abstract

Several recent papers obtained complexity results regarding the geodesic hull number hngd(G) of a graph G. In this paper, we prove that determining whether hngd(G)≤k is W[2]-hard parameterized by k in diameter-two graphs and is W[1]-hard parameterized by tw+k, where tw is the treewidth of G. Despite this, for graphs with bounded treewidth tw, we prove that hngd(G) is computable in polynomial time O((tw+2)tw+5n2tw+5).

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