Recognizing shrinkable complexes is NP-complete

International audienceWe say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (three-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes which are not shrinkable

Shellability is NP-Complete

We prove that for every d >= 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d >= 2 and k >= 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d >= 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes

Advances in Thermoresponsive Polymers

Thermoresponsive polymers, materials able to undergo sharp and often reversible phase separations in response to temperature stimuli, are introducing new paradigms in different fields, including medicine, advanced separations and oil and gas. In "Advances in Thermoresponsive Polymers", a clear picture of the frontiers reached in the understanding of the mechanistic behavior associated with temperature-induced phase separation, the influence of the polymer structure in regulating the macroscopic behavior of these materials and the latest applications for which thermoresponsive polymers show great potential is provided

Cancer Nanomedicine

This special issue brings together cutting edge research and insightful commentary on the currentl state of the Cancer Nanomedicine field

Recognizing Shrinkable Complexes Is NP-Complete

International audienceWe say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (two-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes that are not shrinkable