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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
This note covers the following topics: Background from Graph Theory and Logic, Descriptive Complexity, Treelike Decompositions, Definable Decompositions, Graphs of Bounded Tree Width, Ordered Treelike Decompositions, 3-Connected Components, Graphs Embeddable in a Surface, Definable Decompositions of Graphs with Excluded Minors, Quasi-4-Connected Components, K5-Minor Free Graphs, Completions of Pre-Decompositions, Planar Graphs, Decompositions of Almost Embeddable Graphs
Author(s): Martin Grohe
495 Pages 
A Simple Introduction to Graph Theory
This note covers basics, Proofs, Constructions, Algorithms and applications, Bipartite graphs and trees, Eulerian and Hamiltonian graphs, Coloring, Planar graphs, Digraphs and connectivity.
Author(s): Brian Heinold
134 Pages
Graph Theory by Prof. Dr. Maria Axenovich
This PDF book covers the following topics related to Graph Theory :Preliminaries, Matchings, Connectivity, Planar graphs, Colorings, Extremal graph theory, Ramsey theory, Flows, Random graphs, Hamiltonian cycles.
Author(s): Prof. Dr. Maria Axenovich
104 Pages
Graph Theory by Gordon College
This note explains the following topics: Theorems, Representations of Graphs: Data Structures, Traversal: Eulerian and Hamiltonian Graphs, Graph Optimization, Planarity and Colorings.
Author(s): Gordon College
120 Pages
Extremal Graph Theory for Book Embeddings
This note describes the following topics: Book-Embeddings and Pagenumber, Book-Embeddings of Planar Graphs, Extremal Graph Theory, Pagenumber and Extremal Results, Maximal Book-Embeddings.
Author(s): Jessica McClintock
64 Pages
Graph Theory Lecture Notes by NPTEL
The intension of this note is to introduce the subject of graph theory to computer science students in a thorough way. This note will cover all elementary concepts such as coloring, covering, hamiltonicity, planarity, connectivity and so on, it will also introduce the students to some advanced concepts.
Author(s): NPTEL
NA Pages
Structural Graph Theory Lecture Notes
This note covers the following topics: Immersion and embedding of 2-regular digraphs, Flows in bidirected graphs, Average degree of graph powers, Classical graph properties and graph parameters and their definability in SOL, Algebraic and model-theoretic methods in constraint satisfaction, Coloring random and planted graphs: thresholds, structure of solutions and algorithmic hardness.
Author(s): Andrew Goodall
123 Pages