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Author: Michael A. Henning
Publisher: Springer Nature
ISBN: 3030465594
Category : Mathematics
Languages : en
Pages : 231
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Book Description
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.
Author: Michael A. Henning
Publisher: Springer Nature
ISBN: 3030465594
Category : Mathematics
Languages : en
Pages : 231
Get Book
Book Description
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.
Author: Andrey O. Matveev
Publisher: CRC Press
ISBN: 100095935X
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This original research monograph concerns various aspects of how (based on the decompositions of vertices of hypercube graphs with respect to their symmetric cycles) the vertex sets of related discrete hypercubes, as well as the power sets of the corresponding ground sets, emerge from rank 2 oriented matroids, from underlying rank 2 systems of linear inequalities, and thus literally from arrangements of straight lines crossing a common point on a piece of paper. It reveals some beautiful and earlier-hidden fragments in the true foundations of discrete mathematics. The central observation made and discussed in the book from various viewpoints consists in that 2t subsets of a finite t-element set Et, which form in a natural way a cyclic structure (well, just t subsets that are the vertices of a path in the cycle suffice), allow us to construct any of 2t subsets of the set Et by means of a more than elementary voting procedure expressed in basic linear algebraic terms. The monograph will be of interest to researchers, students, and readers in the fields of discrete mathematics, theoretical computer science, Boolean function theory, enumerative combinatorics and combinatorics on words, combinatorial optimization, coding theory, and discrete and computational geometry.
Author: Minming Li
Publisher: Springer Nature
ISBN: 3031207963
Category : Computers
Languages : en
Pages : 304
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Book Description
This book constitutes the proceedings of the International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2022), for the 16th International Conference on Frontier of Algorithmic Wisdom (FAW) and the third International Joint Conference on Theoretical Computer Science (IJTCS), held in Hong Kong, China, in August 15-19 2022. FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. In addition to four keynote speakers, 26 invited speakers and 19 contributed speakers, IJTCS-FAW2022 organized Forums for undergraduate research, young PhD graduates, young TCS faculty members, female researchers, as well as a forum in Conscious AI and a CSIAM Forum in blockchain. The 19 full papers presented in this book were carefully reviewed and selected from 25 submissions. They were organized in topical sections as follows: Algorithmic Game Theory; Game Theory in Block Chain; Frontiers of Algorithmic Wisdom; Computational and Network Economics.
Author: Teresa W. Haynes
Publisher: Springer Nature
ISBN: 3030588920
Category : Mathematics
Languages : en
Pages : 536
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Book Description
This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.
Author: C. Berge
Publisher: Elsevier
ISBN: 0080880231
Category : Mathematics
Languages : en
Pages : 267
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Book Description
Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.
Author: Anthony Nixon
Publisher: Cambridge University Press
ISBN: 1009096222
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author: Michael A. Henning
Publisher: Springer Science & Business Media
ISBN: 1461465257
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is an excellent resource for students interested in beginning their research in this field. Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems.
Author: Teresa W. Haynes
Publisher: Springer Nature
ISBN: 3031094964
Category : Mathematics
Languages : en
Pages : 655
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Book Description
This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they’ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.
Author: Ralucca Gera
Publisher: Springer
ISBN: 3319976869
Category : Mathematics
Languages : en
Pages : 281
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Book Description
This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate students and established researchers in discrete mathematics who are searching for research ideas and references. Each chapter provides more than a simple collection of results on a particular topic; it captures the reader’s interest with techniques that worked and failed in attempting to solve particular conjectures. The history and origins of specific conjectures and the methods of researching them are also included throughout this volume. Students and researchers can discover how the conjectures have evolved and the various approaches that have been used in an attempt to solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and over 600 references is also included in this volume. This glossary provides an understanding of parameters beyond their definitions and enables readers to discover new ideas and new definitions in graph theory. The editors were inspired to create this series of volumes by the popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,” which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January 2014, at which many of the best-known graph theorists spoke. In an effort to aid in the creation and dissemination of conjectures and open problems, which is crucial to the growth and development of this field, the editors invited these speakers, as well as other experts in graph theory, to contribute to this series.
Author: Qiufen Ni
Publisher: Springer Nature
ISBN: 3031160819
Category : Computers
Languages : en
Pages : 482
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Book Description
This book constitutes the proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management, AAIM 2022, which was held online during August 13-14, 2022. The conference was originally planned to take place in Guangzhou, China, but changed to a virtual event due to the COVID-19 pandemic. The 41 regular papers included in this book were carefully reviewed and selected from 59 submissions.
