Discrete Introductory books on Graph Theory and Combinatorics?

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The discussion centers on a college junior seeking recommendations for introductory books on graph theory and combinatorics, emphasizing their importance for a current research project in theoretical computer science. The individual is encountering complex terms such as counting problems, matchings, and H-coloring, and is looking for resources that explain these concepts in a reader-friendly manner. They mention having a solid mathematical foundation through courses in Analysis and Linear Algebra, which suggests they are prepared for a deeper exploration of these topics. The request highlights the need for accessible materials that cover both theoretical aspects and practical applications of graph theory and combinatorics.
bacte2013
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Dear Physics Forum friends,

I am a college junior who is currently conducting the undergraduate research in the theoretical computer science. I wrote this post to seek you recommendation on the books that separately treat the graph theory and combinatotics, both in theory and applications. I really need to understand the graph theory and combinatotics as it is one of the crucial parts of my current project. I am encountering terms like counting problems, matchings, H-coloring/homomorphisms, 2-3 graphs, etc. I am currently taking Analysis I (Rudin) and Linear Algebra (Hoffman/Kunze) so I have a good degree of mathematical maturity, but I would like books that treat the combinatorics and graph theory in a reader-friendly, introductory levels.
 
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