University of Greifswald, 134 p.
Introduction.
Networks.
Graphs.
Connected graphs.
Degree sequences.
Trees and forests.
The matrix of adjacency.
Planar graphs.
Digraphs.
Further reading.
Labeled Graphs.
All graphs.
The number of connected graphs.
Eulerian graphs.
The number of planar graphs.
Random graphs.
Tournaments.
The Number of Labeled Trees.
Permutations.
Trees with a given degree sequence.
The Pr ufer code.
The number of labeled forests.
Unlabeled Graphs.
Isomorphic graphs.
Labeled and unlabeled graphs.
The number of graphs.
The number of connected graphs.
Polyhedrons.
Regular polyhedrons.
The Number of Unlabeled Trees.
Upper and lower bounds.
Generating functions.
Phylogenetic Networks.
Phylogenetic trees.
Semi-labeled trees.
Double stars.
The structure of rooted trees.
The number of rooted trees.
Generalized binary trees.
Multifurcating trees.
Phylogenetic forests.
The collection of Trees.
Splits and trees.
Consensus Trees.
The metric spaces of all trees.
Further reading.
Spanning trees.
The number of spanning trees.
Generating all spanning trees.
A recursive procedure.
The matrix-tree theorem.
Applications.
Graphs inside.
Subgraph isomorphism.
Trees inside.
Counting perfect matchings.
Alignments.
Forbidden subgraphs.
Ramsey Theory.
Coloring the edges.
Ramsey's theorem.
Known Ramsey numbers.
Asymptotics.
Generalized Ramsey numbers.
