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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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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Abstract 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.
AbstractList 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.
In this paper, we determine the necessary and sufficient conditions for the existence of an equitably -colorable balanced incomplete block design for any positive integer 2. In particular, we present a method for constructing nontrivial equitably -colorable BIBDs and prove that these examples are the only nontrivial examples that exist. We also observe that every equitable -coloring of a BIBD yields both an equalized -coloring and a proper 2-coloring of the same BIBD.
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 . 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.
Author Luther, Robert D.
Pike, David A.
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– reference: V. I. Voloshin, Coloring Mixed Hypergraphs: Theory, Algorithms and Applications, American Mathematical Society, Providence, Rhode Island, 2002.
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Snippet In this paper, we determine the necessary and sufficient conditions for the existence of an equitably ℓ‐colorable balanced incomplete block design for any...
In this paper, we determine the necessary and sufficient conditions for the existence of an equitably -colorable balanced incomplete block design for any...
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SubjectTerms 05C15
block designAMS subject classifications: 05B05
equitable coloring
equitable coloring; block designAMS subject classifications: 05B05
Title Equitably Colored Balanced Incomplete Block Designs
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