13 citations · 32 across the 10 of their papers we have counts for
6 papers · 1 filter
Large Simple d-Cycles in Simplicial Complexes
Roy Meshulam, Ilan Newman, Yuri Rabinovich
We show that the size of the largest simple d-cycle in a simplicial d-complex is at least a square root of 's density. This generalizes a well-known classical result of Erdő…
Hamiltonian and Pseudo-Hamiltonian Cycles and Fillings In Simplicial Complexes
Rogers Mathew, Ilan Newman, Yuri Rabinovich +1
We introduce and study a -dimensional generalization of Hamiltonian cycles in graphs - the Hamiltonian -cycles in (the complete simplicial -complex over a vertex s…
Rational Polygons: Odd Compression Ratio and Odd Plane Coverings
Rom Pinchasi, Yuri Rabinovich
Let P be a polygon with rational vertices in the plane. We show that for any finite odd-sized collection of translates of P, the area of the set of points lying in an odd number of…
Boundaries of Hypertrees, and Hamiltonian Cycles in Simplicial Complexes
Rogers Mathew, Ilan Newman, Yuri Rabinovich +1
A -hypertree on is a maximal acyclic -dimensional simplicial complex with full -skeleton on the vertex set . Alternatively, in the language of algebraic top…
On Connectivity of the Facet Graphs of Simplicial Complexes
Ilan I. Newman, Yuri Rabinovich
The paper studies the connectivity properties of facet graphs of simplicial complexes of combinatorial interest. In particular, it is shown that the facet graphs of -cycles, …
Extremal problems on shadows and hypercuts in simplicial complexes
Nati Linial, Ilan Newman, Yuval Peled +1
Let be an -vertex forest. We say that an edge is in the shadow of if contains a cycle. It is easy to see that if is "almost a tree", that is…