Let the bridge - fragments of G with respect to C be all planar , and let no two bridges of C in G overlap . ... We can now recognize a 2 - separation ( HK ) of G. Here H is the union of L ' and the members of U , and K is the union of ...
This new text introduces basic concepts, definitions, theorems, and examples from graph theory.
Hall's theorem is a very flexible and useful result. ... We now restate Hall's theorem in set terms. ... A set C of vertices is said to cover the edges of a graph G (or be an edge cover), if every edge in G is incident to a vertex in C.
Graph Theory: With Engineering Applications
Graph Theory
This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint.
From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject.
51, 45–64 (1962) Mahadev, N.V.R., Peled, U.N.: Threshold Graphs and Related Topics. North-Holland, Amsterdam (1995) McKee, T., McMorris, F.R.: Topics in Intersection Graph Theory. Society for Industrial and Applied Mathematics, ...
The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.
Graph theory: new frontiers
Graph Theory
For junior- to senior-level courses in Graph Theory taken by majors in Mathematics, Computer Science, or Engineering or for beginning-level graduate courses. Once considered an "unimportant" branch of topology,...
This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory.
Graph Theory: An Algorithmic Approach
It has every chance of becoming the standard textbook for graph theory.” Acta Scientiarum Mathematicarum "Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity.
This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems.
A natural way to learn some of the essential ideas of graph theory from first principles.