mathematics, a bisimplicial set is a simplicial object in the category of simplicial sets, which themselves are simplicial objects in the category of sets. Many...

vertex of a graph is bisimplicial if the set of it and its neighbours is the union of two cliques, and is k-simplicial if the set is the union of k cliques...

simplicial set A {\displaystyle A} define a bisimplicial set and a simplicial set with the opposite simplicial set and the join of simplicial sets by: T w...

al. (2008) demonstrated that every even-cycle-free graph contains a bisimplicial vertex (a vertex whose neighborhood is the union of two cliques), which...

with f ( t ) = 2 t {\displaystyle f(t)=2t} , as every such graph has a bisimplicial vertex, a vertex whose neighborhood is the union of two cliques However...

"Homotopy theory of Γ {\displaystyle \Gamma } -spaces, spectra, and bisimplicial sets", Geometric Applications of Homotopy Theory II, Lecture Notes in Mathematics...

simplicial sets. The geometrical realisation of this is the Artin-Mazur homotopy type. A generalisation of E. Friedlander using bisimplicial hypercoverings...