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math.CO2010★ 11 cited
Collapsibility and vanishing of top homology in random simplicial complexes
L. Aronshtam, N. Linial, T. Luczak +1
Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex inde…
math.CO2005
First Order Definability of Trees and Sparse Random Graphs
Tom Bohman, Alan Frieze, Tomasz Luczak +4
Let D(G) be the smallest quantifier depth of a first order formula which is true for a graph G but false for any other non-isomorphic graph. This can be viewed as a measure for the…