Fractional Graph Theory: A Rational Approach to the Theory of Graphs
by Daniel Ullman, Edward Scheinerman
Publisher: Wiley 2008
Number of pages: 167
The vast majority of concepts in graph theory are whole-number based. Invariants from chromatic number to arboricity only take on integer values. In this book the authors explore generalizations of core graph theory notions by allowing real values to substitute where normally only integers would be permitted. The aim is to prove "fractional analogues" of the theorems of traditional graph theory.
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by Alexander Schrijver
From the table of contents: Shortest trees and branchings; Matchings and covers; Edge-colouring; Multicommodity flows and disjoint paths; Matroids; Perfect matchings in regular bipartite graphs; Minimum circulation of railway stock.
Contents: Introduction; The Basics; Tree; Multigraph; Extremal graph theory; Graph Traversal; Analysis; Example Applications of Graph Theory; Travelling salesman problem; Route inspection problem; Hamiltonian path problem; etc.
by Keijo Ruohonen - Tampere University of Technology
These lecture notes form the base text for a Graph Theory course. The text contains an introduction to basic concepts and results in graph theory, with a special emphasis put on the network-theoretic circuit-cut dualism.
by David Joyner, Minh Van Nguyen, Nathann Cohen - Google Code
An introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source software. The text covers graph algorithms, trees and forests, distance and connectivity, optimal graph traversals, planar graphs, etc.