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Equitably Colored Balanced Incomplete Block Designs
Author(s) -
Luther Robert D.,
Pike David A.
Publication year - 2016
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21427
Subject(s) - mathematics , colored , integer (computer science) , combinatorics , block (permutation group theory) , block design , discrete mathematics , computer science , law , political science , programming language
In 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 ℓ ⩾ 2 . 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.