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In this paper we study the (in)approximability of two distance-based relaxed variants of the maximum clique problem (Max Clique), named Max d-Clique and Max d-Club: A d-clique in a graph $$G = (V, E)$$ G=(V,E) is a subset $$S\subseteq V$$ S⊆V of vertices such that for every pair of vertices $$u, v\in S$$ u,v∈S , the distance between u and v is at most d in G. A d-club in a graph $$G = (V, E)$$ G=(V,E)...
For high-molecular-weight (M) ring polymers with low contamination of linear chains, recent viscoelastic tests revealed broad terminal relaxation associated with no clear entanglement plateau. This relaxation behavior is qualitatively similar to that deduced from molecular models (double-folded lattice-animal model and the fractal loopy globule model) for entangled ring polymers, but quantitatively...
A dumbbell-shaped polystyrene (PS) sample, where rings are attached on both ends of a linear chain, was anionically synthesized by a coupling reaction between highly-purified ring PS (R-30; Mw = 33.7 kg/mol) with two diphenylethylene (DPE) type vinyl groups and bifunctional living linear PS (L-80; Mw = 84.0 kg/mol). The crude coupling product obtained was confirmed to include a targeted dumbbell polymer...
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