I would like to learn a bit of Graph theory for mathematical Olympiads.Can anyone please point out a resource from where I can learn it? Here's my background: I have limited knowledge of linear algebra but I know basic combinatorics including counting, pigeonhole principle, bijection, recursion, counting in two ways etc.I do not mind an elementary but really tough introductory book/resource.Thanks a lot in advance.
Graph Theory And Combinatorics By Grimaldi Pdf 29
For a book length treatment, with practice problems that are challenging, I would highly recommend Douglas West, Introduction to Graph Theory (2nd edition), Prentice-Hall, 2001. However, for a very short but somewhat comprehensive introduction I would recommend the introductory chapter of Graph Connections (ed. Lowell Beineke and Robin Wison), Oxford, 1997. The first chapter by Robin Wilson is 13 pages long. Other chapters connect graphs to groups, geometry, number theory, topology, knots, linear algebra, etc. The exposition is top notch.
Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers.
The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers.
Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.
RALPH P. GRIMALDI, PHD, is Professor of Mathematics at Rose-Hulman Institute of Technology. With more than forty years of experience in academia, Dr. Grimaldi has published numerous articles in discrete mathematics, combinatorics, and graph theory. Over the past twenty years, he has developed and led mini-courses and workshops examining the Fibonacci and the Catalan numbers. Permissions Request permission to reuse content from this site
Sets; relations: equivalence and partial order relations; induction, recurrence, combinatorics, principle for inclusion and exclusion; number theory, modular arithmetic and public key cryptography; graphs.
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