A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d − 1 that is contained in a unique maximal face. We prove that the algorithmic question whether a given simplicial complex is d-collapsible is NP-complete for d ≥ 4 and polynomial time solvable for d ≤ 2. As an intermediate step, we prove that d-collaps...

A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d − 1 that is contained in a unique maximal face. We prove that the algorithmic question whether a given simplicial complex is d-collapsible is NP-complete for d ≥ 4 and polynomial time solvable for d ≤ 2. As an intermediate step, we prove that d-collaps...

The aim of this study was to improve the characteristics natural collapsible soils using geogrid-encased stone column technique. For purpose, 20 large-scale specimens columns were prepared rigid metal cylinders with a diameter 308 mm and height 97 154 according unit cell theory. aspect ratio 10% 25%. occurrence bulging failure, considered six times diameter. encased geogrids varying stiffness f...

Abstract Collapsible soils present significant geotechnical and structural engineering challenges worldwide. They can be found in arid or semi-arid regions are directly affected by the multi-step wetting procedure due to reduction of soil suction. The main objectives this paper investigate volume change behaviour, collapse mechanism deformation characteristics under control suction net vertical...

The use of micropiles has been increasing in recent years, mostly for horizontally loaded cases. Given the little information about this foundation type under lateral top-loading, especially high-porosity and collapsible soils, a total four transversal loading tests were carried out new post-grouted micropile configuration with length 17 m diameter 0.3 m, two natural soil moisture conditions fl...

Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai (Combinatorics and Graph Theory, vol 95, World Scientific, Singapore, pp 53–69; Conjecture 8.6 of 1995) conjectured that every 3-edge connected and essentially 6-edge connected graph is collapsible. Denote D3(G) the set of vertices of degree 3 of graph G. For e = uv ∈ E(G), define d(e) = d(u)+ d(v)− 2 the edge ...

We present a pumping lemma for the class of collapsible pushdown graphs of level 2. This pumping lemma even applies to the ε-contractions of level 2 collapsible pushdown graphs. Our pumping lemma also improves the bounds of Hayashi’s pumping lemma for indexed languages. 1998 ACM Subject Classification F.1.1 Models of Computation