{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T20:34:13Z","timestamp":1722285253774},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p>A subset [Formula: see text] of vertices in a hypergraph [Formula: see text] is a transversal if [Formula: see text] has a nonempty intersection with every edge of [Formula: see text]. The transversal number of [Formula: see text] is the minimum size of a transversal in [Formula: see text]. A subset [Formula: see text] of vertices in a graph [Formula: see text] with no isolated vertex, is a total dominating set if every vertex of [Formula: see text] is adjacent to a vertex of [Formula: see text]. The minimum cardinality of a total dominating set in [Formula: see text] is the total domination number of [Formula: see text]. In this paper, we obtain a new (improved) probabilistic upper bound for the transversal number of a hypergraph, and a new (improved) probabilistic upper bound for the total domination number of a graph.<\/jats:p>","DOI":"10.1142\/s1793830919500046","type":"journal-article","created":{"date-parts":[[2018,11,8]],"date-time":"2018-11-08T02:44:50Z","timestamp":1541645090000},"page":"1950004","source":"Crossref","is-referenced-by-count":1,"title":["A note on improved upper bounds on the transversal number of hypergraphs"],"prefix":"10.1142","volume":"11","author":[{"given":"Michael A.","family":"Henning","sequence":"first","affiliation":[{"name":"Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park, 2006 South Africa"}]},{"given":"Nader Jafari","family":"Rad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahed University, Tehran, Iran"}]}],"member":"219","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"S1793830919500046BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(82)90049-8"},{"key":"S1793830919500046BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01787474"},{"key":"S1793830919500046BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/0471722154"},{"key":"S1793830919500046BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00816-X"},{"key":"S1793830919500046BIB005","volume-title":"Hypergraphs \u2014 Combinatorics of Finite Sets","author":"Berge C.","year":"1989"},{"key":"S1793830919500046BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01191201"},{"key":"S1793830919500046BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.07.016"},{"key":"S1793830919500046BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2015.10.034"},{"key":"S1793830919500046BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.12.044"},{"key":"S1793830919500046BIB011","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1002\/jgt.20340","volume":"59","author":"Henning M. 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