Advanced graph theory and combinatorics
Advanced Graph Theory and Combinatorics by Michel RigoAdvanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.
PMSP - Regularity Lemmas in graph theory, additive combinatorics and TCS I - Luca Trevisan
Advanced Graph Theory and Combinatorics
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Based on a course taught for more than ten years at university level, this book focuses on some of the main notions arising in graph theory, with an emphasis throughout on the possible applications of the theory and the fruitful links that exist with linear algebra. Commencing with basic notions such as connectedness, Eulerian, Hamiltonian and planar graphs, it opens the way for a variety of applications. Many graph theory problems are computationally challenging. Therefore, a short chapter is devoted to complexity theory, and after a presentation of the chromatic polynomial and Ramsey numbers, the book highlights the important interplay between graph theory and linear algebra. Perron-Frobenius theory is then presented.
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