On the Complexity of the Upper r-Tolerant Edge Cover Problem

International audienceWe consider the problem of computing edge covers that are tolerant to a certain number of edge deletions. We call the problem of finding a minimum such cover r-Tolerant Edge Cover (r-EC) and the problem of finding a maximum minimal such cover Upper r-EC. We present several NP-hardness and inapproximability results for Upper r-EC and for some of its special cases

Energetics and structure of grain boundary triple junctions in graphene

Grain boundary triple junctions are a key structural element in polycrystalline materials. They are involved in the formation of microstructures and can influence the mechanical and electronic properties of materials. In this work we study the structure and energetics of triple junctions in graphene using a multiscale modelling approach based on combining the phase field crystal approach with classical molecular dynamics simulations and quantum-mechanical density functional theory calculations. We focus on the atomic structure and formation energy of the triple junctions as a function of the misorientation between the adjacent grains. We find that the triple junctions in graphene consist mostly of five-fold and seven-fold carbon rings. Most importantly, in addition to positive triple junction formation energies we also find a significant number of orientations for which the formation energy is negative.Peer reviewe