## Tesi etd-09132011-145916 |

Thesis type

Tesi di laurea magistrale

Author

CARACENI, ALESSANDRA

URN

etd-09132011-145916

Title

Lagrangians of Hypergraphs

Struttura

SCIENZE MATEMATICHE, FISICHE E NATURALI

Corso di studi

MATEMATICA

Commissione

**controrelatore**Prof. Gaiffi, Giovanni

**relatore**Prof. Dvornicich, Roberto

Parole chiave

- hypergraph lagrangian
- graph
- hypergraph
- combinatorics
- extremal graph theory
- Turan problem

Data inizio appello

30/09/2011;

Consultabilità

completa

Riassunto analitico

The Lagrangian of a hypergraph is a function that in a sense seems to measure how ‘tightly packed’ a subset of the hypergraph one can find. Lagrangians were first used by Motzkin and Straus to obtain a new proof of a classic theorem of Turán, and subsequently found a number of very valuable applications in Extremal Hypergraph Theory; one remarkable result they yield is the disproof of a famous "jumping conjecture" of Erdos, which we reprove entirely; we will also introduce a very recent method based on Razborov's flag algebras to show that, though the jumping conjecture is false in general, hypergraphs "do jump" in some cases.

File

Nome file | Dimensione |
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Lagrangi...raphs.pdf | 501.96 Kb |

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