Modern Graph Theory

  title={Modern Graph Theory},
  author={B{\'e}la Bollob{\'a}s},
  booktitle={Graduate Texts in Mathematics},
  • B. Bollobás
  • Published in Graduate Texts in Mathematics 2002
  • Mathematics
This text is an in-depth account of graph theory. It reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as colouring, matching, extremal theory, and… 

An introduction to the theory of random graphs

This thesis provides an introduction to the fundamentals of random graph theory with results such as Mycielski's construction of a family of triangle-free graphs with high chromatic number and results in Ramsey theory.

Structural Graph Theory

It is proved that a condition of minimum degree for the vertices and the ends of the graph ensure the existence of a complete graph as a minor and as a topological minor in an infinite graph.

Graph-Theoretic Foundations

This chapter presents the necessary graph-theoretic foundations for the research presented in the remainder of the monograph, followed by three separate sections on graph matching, graph isomorphism, and network flow.

Combinatorial evaluations of the Tutte polynomial

The Tutte polynomial is one of the most important and most useful invariants of a graph. It was discovered as a two variable generalization of the chromatic polynomial [15, 16], and has been studied

Spectral Properties of Graphs

In this chapter, we look at the properties of graphs from our knowledge of their eigenvalues. The set of eigenvalues of a graph G is known as the spectrum of G and denoted by Sp(G). We compute the

Metrized graphs, electrical networks, and Fourier analysis

This expository paper studies the Laplacian operator on a metrized graph and some important functions related to it, including the ``j-function'', the effective resistance, and eigenfunctions of the LaPLacian.

Graph Polynomials and Graph Transformations in Algebraic Graph Theory

The main results of this thesis show that the Kelmans transformation is a very effective tool in many extremal alge- braic graph theoretic problems and attain a breakthrough in a problem of Eva Nosal by the aid of this transformation.

A logician's view of graph polynomials

The interlace polynomial of a graph