Equitably Colored Balanced Incomplete Block Designs

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 ar...

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Bibliographic Details
Published inJournal of combinatorial designs Vol. 24; no. 7; pp. 299 - 307
Main Authors Luther, Robert D., Pike, David A.
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.07.2016
Wiley Subscription Services, Inc
Subjects
05C15
block designAMS subject classifications: 05B05
equitable coloring
equitable coloring; block designAMS subject classifications: 05B05
Online AccessGet full text
ISSN1063-8539
1520-6610
DOI10.1002/jcd.21427

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Summary: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.
Bibliography:ark:/67375/WNG-2ST0GFQ8-P
ArticleID:JCD21427
istex:EF045AAF81B5922FA998D38CEE7F06646FBF4122
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.21427