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Author | : Denes König |
Publisher | : Springer Science & Business Media |
Total Pages | : 430 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1468489712 |
Download Theory of Finite and Infinite Graphs Book in PDF, ePub and Kindle
To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale . . . " 10]. There were earlier books that took note of graph theory. Veb len's Analysis Situs, published in 1931, is about general combinato rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes," are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such. But the honour of presenting Graph Theory to the mathe matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse ment, how one mathematician scorned it as "The slums of Topol ogy.""
Author | : Dénes König |
Publisher | : |
Total Pages | : 426 |
Release | : 1990-01-01 |
Genre | : Graph theory |
ISBN | : 9783764333898 |
Download Theory of Finite and Infinite Graphs Book in PDF, ePub and Kindle
Author | : R. Diestel |
Publisher | : Elsevier |
Total Pages | : |
Release | : 2016-06-06 |
Genre | : Mathematics |
ISBN | : 148329479X |
Download Directions in Infinite Graph Theory and Combinatorics Book in PDF, ePub and Kindle
This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.
Author | : Wolfgang Woess |
Publisher | : Cambridge University Press |
Total Pages | : 350 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 0521552923 |
Download Random Walks on Infinite Graphs and Groups Book in PDF, ePub and Kindle
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Author | : Martin Charles Golumbic |
Publisher | : Springer Nature |
Total Pages | : 122 |
Release | : 2021-02-09 |
Genre | : Mathematics |
ISBN | : 3030614204 |
Download The Zeroth Book of Graph Theory Book in PDF, ePub and Kindle
Marking 94 years since its first appearance, this book provides an annotated translation of Sainte-Laguë's seminal monograph Les réseaux (ou graphes), drawing attention to its fundamental principles and ideas. Sainte-Laguë's 1926 monograph appeared only in French, but in the 1990s H. Gropp published a number of English papers describing several aspects of the book. He expressed his hope that an English translation might sometime be available to the mathematics community. In the 10 years following the appearance of Les réseaux (ou graphes), the development of graph theory continued, culminating in the publication of the first full book on the theory of finite and infinite graphs in 1936 by Dénes König. This remained the only well-known text until Claude Berge's 1958 book on the theory and applications of graphs. By 1960, graph theory had emerged as a significant mathematical discipline of its own. This book will be of interest to graph theorists and mathematical historians.
Author | : Gena Hahn |
Publisher | : |
Total Pages | : 276 |
Release | : 1989-12-31 |
Genre | : |
ISBN | : 9789400905184 |
Download Cycles and Rays Book in PDF, ePub and Kindle
Author | : Koh Khee Meng |
Publisher | : World Scientific Publishing Company |
Total Pages | : 244 |
Release | : 2007-03-15 |
Genre | : Mathematics |
ISBN | : 9813101636 |
Download Introduction to Graph Theory Book in PDF, ePub and Kindle
Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Author | : Luis Ribes |
Publisher | : Springer |
Total Pages | : 471 |
Release | : 2017-08-23 |
Genre | : Mathematics |
ISBN | : 3319611992 |
Download Profinite Graphs and Groups Book in PDF, ePub and Kindle
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.
Author | : Peter G. Doyle |
Publisher | : American Mathematical Soc. |
Total Pages | : 159 |
Release | : 1984-12-31 |
Genre | : Electric network topology |
ISBN | : 1614440220 |
Download Random Walks and Electric Networks Book in PDF, ePub and Kindle
Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Author | : Norbert W Sauer |
Publisher | : Springer Science & Business Media |
Total Pages | : 452 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401120803 |
Download Finite and Infinite Combinatorics in Sets and Logic Book in PDF, ePub and Kindle
This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.