On the domination of hypergraphs by their edges

✍ Scribed by A. Behr; L. Camarinopoulos

• Book ID: 104114003
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 395 KB
• Volume: 187
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(97)00244-6

✦ Synopsis

Given a hypergraph 9f=(E1,...,Er,) with vertex set V, let no be the number of different possibilities for coveting V by an odd number of E's and n~ the number of different possibilities for covering V when selecting an even number of E's. The quantity d(V, o~f)= no-n¢ is known as the (reliability) domination of ~f~ and a combinatorial invariant of considerable practical relevance. The present paper addresses the problem to determine this domination. After reviewing the current theory in the area we present some new relationships for d(V,;,~) with respect to dual and interval hypergraphs.