##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Gyula Y. Katona

#### Alfr'ed R'enyi Institute of Mathematics \\ Hungarian Academy of Sciences

## Hamiltoninan Chains in Hypergraphs

##### Abstract:

An r-uniform hypergraph is a generalization of graphs, we consider a subset of all r-element subsets of a given vertex set. A Hamiltionian chain is a generalization of hamiltonian cycles for hypergraphs, it is a "cycle" that contains all vertices. Among the several possible ways of generalizations this is probably the most strong one, it requires the strongest structure. Since there are many interesting questions about hamiltonian cycles in graphs, we can try to answer these questions for hypergraphs, too. I give a survey on results about such questions.

Host: Fan Chung Graham

### May 1, 2007

### 4:00 PM

### AP&M 7321

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