Add to ORKGIn a seminal paper Kalai (1983) extended the notion of a tree to higher dimensions. Formally, an n-vertex d-dimensional hypertee is a Q-acyclic simplicial complex with a full (d-1) dimensional skeleton and {n-1 \choose d} d-dimensional faces. We will use instead an equivalent intuitive definition that relies only on elementary linear algebra. In this talk I will try to give a flavor of these exciting concepts. I will discuss several of the many open problems that arise here and describe some of our new discoveries. My coauthors in the relevant papers are: R. Meshulam, Y. Peled, M. Rosenthal, I. Newman and Y. Rabinovich.Non UBCUnreviewedAuthor affiliation: Hebrew University of JerusalemFacult
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a ...
This thesis is dedicated to the combinatorial, algebraic and homological study of hypertrees and sem...
Abstract. This paper surveys recent results related to the concept of hypertree decomposition and th...
AbstractVarious generalizations of tree-characterization theorems are developed for n-dimensional co...
Abstract A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k − 1)-di...
Let F be an n-vertex forest. We say that an edge e / ∈ F is in the shadow of F if F ∪{e} contains a ...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the se...
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a ...
In the first part of the thesis, we introduce a family of simplicial complexes called tree complexe...
Cette thèse est consacrée à l’étude combinatoire, algébrique et homologique des hyperarbres et des p...
Let V be a n-set (set of size n). Let E be the collection of all possible k-subsets (subsets of size...
AbstractThe graphs known as trees have natural analogues in higher dimensional simplicial complexes....
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a ...
This thesis is dedicated to the combinatorial, algebraic and homological study of hypertrees and sem...
Abstract. This paper surveys recent results related to the concept of hypertree decomposition and th...
AbstractVarious generalizations of tree-characterization theorems are developed for n-dimensional co...
Abstract A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k − 1)-di...
Let F be an n-vertex forest. We say that an edge e / ∈ F is in the shadow of F if F ∪{e} contains a ...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much...
We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the se...
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a ...
In the first part of the thesis, we introduce a family of simplicial complexes called tree complexe...
Cette thèse est consacrée à l’étude combinatoire, algébrique et homologique des hyperarbres et des p...
Let V be a n-set (set of size n). Let E be the collection of all possible k-subsets (subsets of size...
AbstractThe graphs known as trees have natural analogues in higher dimensional simplicial complexes....
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a ...
This thesis is dedicated to the combinatorial, algebraic and homological study of hypertrees and sem...
Abstract. This paper surveys recent results related to the concept of hypertree decomposition and th...