Planar Graphs: Theory and Algorithms

Description

Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.



Included in series:

Annals of Discrete Mathematics, 32

North-Holland Mathematics Studies, 140



Contents



Graph Theoretic Foundations.

Some Basic Definitions. Planar Graphs. Euler's Formula. Kuratowski's Theorem. Dual Graphs. Bounds for Planar Graphs.



Algorithmic Foundations.

What is an Algorithm? Machine Model and Complexity. NP-Complete. Data Structure and Graph Representation. Exploring a Graph.



Planarity Testing and Embedding.

Planarity Testing. Embedding Algorithm.



Drawing Planar Graphs.

Convex Drawing. Convex Testing. Example.



Vertex-Coloring.

Proof of Five-Coloring Theorem and 0(n2) Algorithm. Batch Processing Algorithm. Sequential Processing Algorithm.



Edge-Coloring.

Algorithm COLOR. Algorithm ALCOLOR. Edge-Coloring Multigraphs.



Independent Vertex Sets.

Approximation Algorithm. Baker's Algorithm.



Listing Subgraphs.

Arboricity and Efficient Edge-Searching. Listing Triangles. Listing Quadrangles. Listing Maximal Cliques.



Planar Separator Theorem.

Applications of the Planar Separator Theorem. Maximum Matching. Minimum Vertex Cover.



Hamiltonian Cycles.

Proof of Tutte's Theorem. Algorithm and 0(n2) Bound. Hamiltonian Walk.



Flows in Planar Graphs.

Definition of Multicommodity Flows. Planar Single-Commodity Flow. Multicommodity Flows for C1. Multicommodity Flows for Ca. Bibliography. Index.

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