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Coloring Four-uniform Hypergraphs on Nine Vertices

Published online by Cambridge University Press:  20 November 2018

Marek Kazimierz Lewkowicz
Marek Kazimierz Lewkowicz*
Affiliation:
Faculty of Mechanical and Power Engineering, Wrocław University of Technology, 50-370 Wrocław, Poland. e-mail: marek.lewkowicz@pwr.edu.pl
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Abstract

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Every 4-uniform hypergraph on 9 vertices with at most 25 edges has property $\text{B}$. This gives the answer ${{m}_{9}}\left( 4 \right)\,=\,26$ to a question raised by Erdős in 1968.

Keywords

05C15property Bcoloring hypergraphs
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 317 - 319
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Abbott, H. L. and Liu, A. C., On property B of families of sets. Canad. Math. Bull. 23 (1980), no. 4, 429–435. http://dx.doi.org/10.4153/CMB-1980-063-6 Google Scholar
[2] de Vries, H.L., On property Bandon Steiner systems. Math. Z. 153 (1977), no. 2, 155–159. http://dx.doi.Org/10.1007/BF01179788 Google Scholar
[3] Erdôs, P., On a combinatorial problem. II. Acta Math. Acad. Sci. Hungar 15 (1964), 445^47. http://dx.doi.Org/10.1007/BF01897152 Google Scholar
[4] Erdôs, P., On a combinatorial problem. III. Canad. Math. Bull. 12 (1969), 413–416. http://dx.doi.org/10.4153/CMB-1969-051-5 Google Scholar