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ehrenfest
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I have taken an undergraduate course in combinatorics (and graph theory). I am looking for a graduate-level text at that does everything completely rigorouslym and is suitable for self-study. Any suggestions?
Combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects or elements without repetition. Graph theory is a subfield of combinatorics that studies graphs, which are mathematical structures used to model pairwise relationships between objects.
Combinatorics and graph theory have numerous applications in various fields, including computer science, operations research, and statistics. They provide tools and techniques for solving problems involving discrete structures, making them essential in problem-solving and decision-making processes.
Combinatorics and graph theory are used to solve problems in a wide range of fields, such as network design, scheduling, coding theory, and cryptography. They are also applied in social networks, transportation systems, and biological networks to analyze and understand complex relationships and structures.
Some widely used texts for graduate-level combinatorics and graph theory include "Combinatorics and Graph Theory" by John Harris, Jeffry L. Hirst, and Michael S. Mossinghoff, "Introduction to Graph Theory" by Douglas West, and "Enumerative Combinatorics" by Richard P. Stanley.
Typically, a strong background in undergraduate mathematics, including calculus, linear algebra, abstract algebra, and discrete mathematics, is required for studying combinatorics and graph theory at the graduate level. Familiarity with basic concepts in computer science and probability theory is also beneficial.