Books in Discrete mathematics combinatorics

Graph Colouring and Variations

1st Edition
Volume 39
January 1, 1989
D. de Werra + 1 more
English
eBook
9 7 8 0 0 8 0 8 6 7 7 9 3

Graph Theory in Memory of G.A. Dirac

1st Edition
Volume 41
December 1, 1988
L. Døvling Andersen + 4 more
English
eBook
9 7 8 0 0 8 0 8 6 7 8 1 6

This volume is a tribute to the life and mathematical work of G.A. Dirac (1925-1984). One of the leading graph theorists, he developed methods of great originality and made many fundamental discoveries.The forty-two papers are all concerned with (or related to) Dirac's main lines of research. A number of mathematicians pay tribute to his memory by presenting new results in different areas of graph theory. Among the topics included are paths and cycles, hamiltonian graphs, vertex colouring and critical graphs, graphs and surfaces, edge-colouring, and infinite graphs.Some of the papers were originally presented at a meeting held in Denmark in 1985. Attendance being by invitation only, some 55 mathematicians from 14 countries participated in various lectures and discussions on graph theory related to the work of Dirac. This volume contains contributions from others as well, so should not be regarded only as the proceedings of that meeting. A problems section is included, as well as a listing of Dirac's own publications.

Unimodality, Convexity, and Applications

1st Edition
July 28, 1988
Sudhakar Dharmadhikari + 1 more
English
eBook
9 7 8 0 0 8 0 9 1 7 6 6 5

In this book, the basic notions and tools of unimodality as they relate to probability and statistics are presented. In addition, many applications are covered; these include the use of unimodality to obtain monotonicity properties of power functions of multivariate tests, minimum volume confidence regions, and recurrence of symmetric random walks. The diversity of the applications will convince the reader that unimodality and convexity form an important tool in the hands of a researcher in probability and statistics.

Planar Graphs

1st Edition
Volume 32
April 1, 1988
T. Nishizeki + 1 more
English
eBook
9 7 8 0 0 8 0 8 6 7 7 4 8

Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

Recent Results in the Theory of Graph Spectra

1st Edition
Volume 36
January 1, 1988
D.M. Cvetkovic + 3 more
English
eBook
9 7 8 0 0 8 0 8 6 7 7 6 2

The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2.Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

Graph Theory and Applications

1st Edition
Volume 38
January 1, 1988
J. Akiyama + 2 more
English
eBook
9 7 8 0 0 8 0 8 6 7 7 8 6

Matching Theory

1st Edition
Volume 29
June 1, 1986
M.D. Plummer + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 3 2 2

This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

Combinatorics '84

1st Edition
January 1, 1986
M. Biliotti + 4 more
English
eBook
9 7 8 0 0 8 0 8 7 2 3 4 6

Interest in combinatorial techniques has been greatly enhanced by the applications they may offer in connection with computer technology. The 38 papers in this volume survey the state of the art and report on recent results in Combinatorial Geometries and their applications.Contrib... V. Abatangelo, L. Beneteau, W. Benz, A. Beutelspacher, A. Bichara, M. Biliotti, P. Biondi, F. Bonetti, R. Capodaglio di Cocco, P.V. Ceccherini, L. Cerlienco, N. Civolani, M. de Soete, M. Deza, F. Eugeni, G. Faina, P. Filip, S. Fiorini, J.C. Fisher, M. Gionfriddo, W. Heise, A. Herzer, M. Hille, J.W.P. Hirschfield, T. Ihringer, G. Korchmaros, F. Kramer, H. Kramer, P. Lancellotti, B. Larato, D. Lenzi, A. Lizzio, G. Lo Faro, N.A. Malara, M.C. Marino, N. Melone, G. Menichetti, K. Metsch, S. Milici, G. Nicoletti, C. Pellegrino, G. Pica, F. Piras, T. Pisanski, G.-C. Rota, A. Sappa, D. Senato, G. Tallini, J.A. Thas, N. Venanzangeli, A.M. Venezia, A.C.S. Ventre, H. Wefelscheid, B.J. Wilson, N. Zagaglia Salvi, H. Zeitler.

Cycles in Graphs

1st Edition
Volume 27
August 1, 1985
B.R. Alspach + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 2 6 1

This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.

Analysis and Design of Algorithms for Combinatorial Problems

1st Edition
Volume 25
May 1, 1985
G. Ausiello + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 2 0 9

Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed.The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.

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