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**On colorings of non-uniform hypergraphs without short cycles.**
*(English)*
Zbl 1274.05174

Nešetřil, Jarik (ed.) et al., Extended abstracts of the sixth European conference on combinatorics, graph theory and applications, EuroComb 2011, Budapest, Hungary, August 29 – September 2, 2011. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 38, 749-754 (2011).

Summary: The work deals with a generalization of Erdős-Lovász problem concerning colorings of non-uniform hypergraphs. Let \(H=(V,E)\) be a hypergraph and let \(f_r(H)=\sum_{e\in E}r^{1-|e|}\) for some \(r\geq 2\). Erdős and Lovász asked about the value \(f(n)\) equal to the minimum possible value of \(f_2(H)\) where \(H\) is a 3-chromatic hypergraph with minimum edge-cardinality \(n\). In our paper we study a similar problem in the class of hypergraphs with large girth.

For the entire collection see [Zbl 1242.05003].

For the entire collection see [Zbl 1242.05003].

### References:

[1] | Erdos, P., and Lovász, L., Problems and results on 3-chromatic hypergraphs and some related questions, Infinite and Finite Sets, Colloquia Mathematica Societatis Janos Bolyai 10 (1973), 609-627. |

[2] | Beck, J.: On 3-chromatic hypergraphs. Discrete mathematics 24, 127-137 (1978) · Zbl 0429.05055 |

[3] | Lu, L., On a problem of Erdos and Lovász on coloring non-uniform hypergraphs, submitted, preprint is available at www.math.sc.edu/ lu/papers/. |

[4] | Radhakrishnan, J.; Srinivasan, A.: Improved bounds and algorithms for hypergraph two-coloring. Random structures and algorithms 16, 4-32 (2000) · Zbl 0942.05024 |

[5] | Spencer, J. H.: Coloring n-sets red and blue. J. combinatorial theory, series A 30, 112-113 (1981) · Zbl 0448.05032 |

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