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For k≥ 3, let H be a k-uniform connected hypergraph on n vertices and m edges. The transversal number τ(H) is the minimum number of vertices that intersect every edge. We prove the following inequality: τ(H)≤(k-1)m+1k. Furthermore, the extremal hypergraphs with equality holds are exactly hypertrees with perfect matching. Based on the proofs, some combinatorial algorithms on the transversal number are designed. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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ISSN： 0302-9743
Year： 2022
Volume： 13513 LNCS
Page： 376-387
Language： English
0 . 4 0 2
JCR@2005
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