Table of Contents

1 ABC of Graph Theory.- 2 Trees.- 3 Independence and Coverings.- 4 Connectivity.- 5 Matroids.- 6 Planarity.- 7 Graph Traversals.- 8 Degree Sequences.- 9 Graph Colorings.- 10 Directed Graphs.- 11 Hypergraphs.- Answers to Chapter 1: ABC of Graph Theory.- 1.1 Graphs: Basic Notions.- 1.2 Walks, Paths, Components.- 1.3 Subgraphs and Hereditary Properties of Graphs. Reconstructibility.- 1.4 Operations on Graphs.- 1.5 Matrices Associated with Graphs.- 1.6 Automorphism Group of Graph.- Answers to Chapter 2: Trees.- 2.1 Trees: Basic Notions.- 2.2 Skeletons and Spanning Trees.- Answers to Chapter 3: Independence and Coverings.- 3.1 Independent Vertex Sets and Cliques.- 3.2 Coverings.- 3.3 Dominating Sets.- 3.4 Matchings.- 3.5 Matchings in Bipartite Graphs.- Answers to Chapter 4: Connectivity.- 4.1 Biconnected Graphs and Biconnected Components.- 4.3 Cycles and Cuts.- Answers to Chapter 5: Matroids.- 5.1 Independence Systems.- 5.2 Matroids.- 5.3 Binary Matroids.- Answers to Chapter 6: Planarity.-6.1 Embeddings of Graphs. Euler Formula.- 6.2 Plane Triangulation.- 6.3 Planarity Criteria.- 6.4 Duality and Planarity.- 6.5 Measures of Displanarity.- Answers to Chapter 7: Graph Traversals.- 7.1 Eulerian Graphs.- 7.2 Hamiltonian Graphs.- Answers to Chapter 8: Degree Sequences.- 8.1 Graphical Sequences.- 8.3 Split and Threshold Graphs.- 8.4 Degree Sets and Arity Partitions.- Answers to Chapter 9: Graph Colorings.- 9.1 Vertex Coloring.- 9.2 Chromatic Polynomial.- 9.3 Edge Coloring.- 9.4 Colorings of Planar Graphs.- 9.5 Perfect Graphs.- Answers to Chapter 10: Directed Graphs.- 10.1 Directed Graphs: Basic Notions.- 10.2 Reachability and Components.- 10.3 Matrices Associated with Digraph.- 10.4 Tours and Paths.- 10.5 Tournaments.- 10.6 Base and Kernel.- Answers to Chapter 11: Hypergraphs.- 11.1 Hypergraphs: Basic Notions.- 11.2 Hypergraph Realizations.- Notations.