Equitably Colored Balanced Incomplete Block Designs

descriptionPublicationkeyboard_double_arrow_right Article 17 Apr 2015 English Publisher:WileyJournal:Journal of Combinatorial Designs, volume 24, pages 299-307 (issn: 1063-8539, eissn: 1520-6610,

Copyright policy )Funded by:NSERC | unidentified

Authors: Luther, Robert D.; Pike, David A.;

doi: 10.1002/jcd.21427

Equitably Colored Balanced Incomplete Block Designs

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Abstract

AbstractIn this paper, we determine the necessary and sufficient conditions for the existence of an equitably ℓ‐colorable balanced incomplete block design for any positive integer. In particular, we present a method for constructing nontrivial equitably ℓ‐colorable BIBDs and prove that these examples are the only nontrivial examples that exist. We also observe that every equitable ℓ‐coloring of a BIBD yields both an equalized ℓ‐coloring and a proper 2‐coloring of the same BIBD.

Related Organizations

Memorial University of Newfoundland
Canada

Keywords

equitable coloring, Coloring of graphs and hypergraphs, block design, Combinatorial aspects of block designs

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