Authors:
- One of the first books to give strong non-trivial bounds on the transversal number for linear hypergraphs
- Provides the reader with state-of-the-art on transversals in linear uniform hypergraphs
- Familiarizes the student with the subject, the research techniques, and the major accomplishments in the field including photographs of several researchers who made important contributions to the subject
- May lead to further study of those problems which have not been solved completely, and may also inspire the readers to raise new questions and research directions
Part of the book series: Developments in Mathematics (DEVM, volume 63)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
This book gives the state-of-the-art on transversals in linear uniform hypergraphs. The notion of transversal is fundamental to hypergraph theory and has been studied extensively. Very few articles have discussed bounds on the transversal number for linear hypergraphs, even though these bounds are integral components in many applications. This book is one of the first to give strong non-trivial bounds on the transversal number for linear hypergraphs. The discussion may lead to further study of those problems which have not been solved completely, and may also inspire the readers to raise new questions and research directions.
The book is written with two readerships in mind. The first is the graduate student who may wish to work on open problems in the area or is interested in exploring the field of transversals in hypergraphs. This exposition will go far to familiarize the student with the subject, the research techniques, and the major accomplishments in the field. The photographs included allow the reader to associate faces with several researchers who made important discoveries and contributions to the subject. The second audience is the established researcher in hypergraph theory who will benefit from having easy access to known results and latest developments in the field of transversals in linear hypergraphs.
Reviews
“The book is well written, all the proofs are clear and often illustrated with pictures, that makes them easier to follow. I recommend this book to the researchers in the area of hypergraphs – it may serve as a nice survey on the recent results about the transversals in linear hypergraphs. I also think that it would be very useful for graduate students that would like to get familiar with this topic.” (Marcin Anholcer, zbMATH 1454.05003, 2021)
Authors and Affiliations
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Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, South Africa
Michael A. Henning
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Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark
Anders Yeo
About the authors
Anders Yeo is a world-leader in several areas within mathematics and computer science, including total domination in graphs and transversal in hypergraphs, digraphs and algorithms. He has been a plenary and invited speaker at several international conferences and is a prolific researcher having published over 150 papers to date in international mathematics journals. Anders was born in Australia and schooled in Denmark having obtained his PhD at Odense University in December 1997. Thereafter Anders has worked at the University of Victoria in Canada, the University of Aarhus in Denmark, Royal Holloway, University of London, in the UK, the University of Johannesburg in South Africa and the Singapore University of Technology and Design in Singapore. Currently Anders is a professor of Mathematics at the University of Southern Denmark in Denmark.
Bibliographic Information
Book Title: Transversals in Linear Uniform Hypergraphs
Authors: Michael A. Henning, Anders Yeo
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-030-46559-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-46558-2Published: 29 July 2020
Softcover ISBN: 978-3-030-46561-2Published: 30 July 2021
eBook ISBN: 978-3-030-46559-9Published: 28 July 2020
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XV, 229
Number of Illustrations: 26 b/w illustrations, 14 illustrations in colour
Topics: Graph Theory