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Semi-Strong Colouring of Intersecting Hypergraphs

Published online by Cambridge University Press:  24 October 2013

ERIC BLAIS ,
AMIT WEINSTEIN  and
YUICHI YOSHIDA
ERIC BLAIS
Affiliation:
Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, USA (e-mail: eblais@csail.mit.edu)
AMIT WEINSTEIN
Affiliation:
Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: amitw@tau.ac.il)
YUICHI YOSHIDA
Affiliation:
National Institute of Informatics, Tokyo 101-8430, Japan and Preferred Infrastructure, Inc., Tokyo 113-0033, Japan (e-mail: yyoshida@nii.ac.jp)
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Abstract

For any c ≥ 2, a c-strong colouring of the hypergraph G is an assignment of colours to the vertices of G such that, for every edge e of G, the vertices of e are coloured by at least min{c,|e|} distinct colours. The hypergraph G is t-intersecting if every two edges of G have at least t vertices in common.

A natural variant of a question of Erdős and Lovász is: For fixed c ≥ 2 and t ≥ 1, what is the minimum number of colours that is sufficient to c-strong colour any t-intersecting hypergraphs? The purpose of this note is to describe some open problems related to this question.

Keywords

Primary 05C15Secondary 05D40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 1 , January 2014 , pp. 1 - 7
Copyright
Copyright © Cambridge University Press 2013 

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References

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