A hyperedge coloring and application in combinatorial testing

• Published in: AKCE international journal of graphs and combinatorics Vol. 19; no. 2; pp. 125 - 132
• Main Author: Akhtar, Yasmeen
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 04.05.2022
• Subjects: balanced hypergraph; covering array on hypergraph; equitable coloring; Uniform coloring
• ISSN: 0972-8600; 2543-3474; 2543-3474
• DOI: 10.1080/09728600.2022.2081523

For a hypergraph H, a uniform k-coloring of hyperedges always has the same (to within 1) number of hyperedges of each color, whereas an equitable k-coloring of hyperedges has the property that at every vertex all the colors incident the same number of times (to within 1). For every [Formula: see text] the r-uniform complete r-partite hypergraph [Formula: see text] always admits an equitable k-coloring of hyperedges that is also uniform. This paper establishes the existence of an equitable and uniform coloring of hyperedges in a 3-uniform complete tripartite (multi)hypergraph such that the hyperedges of the same color form a connected partial hypergraph with the property that subhypergraph induced by a pair of parts of its vertex set is a complete bipartite graph. Further, we use this coloring for introducing a new hyperedge-hooking operation to construct optimal size mixed covering arrays on hypergraphs.