Ample simplicial complexes

Abstract Motivated by potential applications in network theory, engineering and computer science, we study r -ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property of indestructibility, sense that removing any number its simplexes leaves isomorphic itself. We prove an is simply connected 2-connected for large. The n vertexes satisfies $$\exp \bigl (\Omega (\frac{2^r}{\sqrt{r}}\bigr )\bigr )$$ exp ( Ω 2 r ) . use probabilistic method establish existence with $$n>r 2^r 2^{2^r}$$ n > Finally, introduce iterated Paley , are explicitly constructed nearly optimal vertexes.