For junior- to senior-level courses in Graph Theory taken by majors in Mathematics, Computer Science, or Engineering or for beginning-level graduate courses. Once considered an "unimportant" branch of topology, graph theory has come into its own through many important contributions to a wide range of fields and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; cover design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic.
Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
... Handbook of Computational Group Theory David M. Jackson and Terry I. Visentin, An Atlas of Smaller Maps in Orientable and Nonorientable Surfaces Richard E. Klima, Ernest Stitzinger, and Neil P. Sigmon, Abstract Algebra Applications ...
Hall's theorem is a very flexible and useful result. ... We now restate Hall's theorem in set terms. ... A set C of vertices is said to cover the edges of a graph G (or be an edge cover), if every edge in G is incident to a vertex in C.
Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises.
Introduction to Graph Theory
Filled with exercises and illustrations, Basic Graph Theory is a valuable resource for any undergraduate student to understand and gain confidence in graph theory and its applications to scientific research, algorithms and problem solving.
O'Connor J. J. and Robertson E. F., Leonhard Euler http://www-history.mcs.st-and.ac.uk/Biographies/Euler.html O'Connor J. J. and Robertson E. F., Sir William Rowan Hamilton ... Posa L., A theorem concerning Hamilton lines. Magyar Tud.
From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject.
Edward A. Bender — and E. R. Canfield (1986). The asymptotic number of rooted maps on a surface, J. Combin. Theory Ser. A 43, 244-257. —- and L. B. Richmond (1986). A survey of the asymptotic behavior of maps, J. Combin. Theory Ser.
This volume presents a concise yet comprehensive treatment, featuring complete proofs for almost all of its results and numerous exercises. 1978 edition.