Graph Colorings

Graph theory would not be what it is today if there had been no coloring problems. In fact, a major portion of the 20th-century research in graph theory has its origin in the four-color problem. (See Chapter VIII for details.)

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S. Axler F. W. Gehring K.A. Ribert

Springer Science+Business Media, LLC

Universitext Editors (North America): S. Axler, F.w. Gehring, and K.A. Ribet AksoylKhamsi: Nonstandard Methods in Fixed Point Theory Anderssoo: Topics in Complex Analysis Aupetit: A Primer on Spectral Theory Balakrisboan/Raogaoatbao: A Textbook of Graph Theory Balser: Formal Power Series and Linear Systems ofMeromorphic Ordinary Differential Equations Bapat: Linear Algebra and Linear Models (2nd ed.) Berberiao: Fundarnentals of Real Analysis BoossIBleecker: Topology and Analysis Borkar: Probability Theory: An Advanced Course BOttcberlSilbermaoo: lntroduction to Large Truncated Toeplitz Matrices CarlesoolGamelin: Complex Dynamics Cecil: Lie Sphere Geometry: With Applications to Submanifolds Cbae: Lebesgue lntegration (2nd ed.) Cbarlap: Bieberbach Groups and Flat Manifolds Cbem: Complex Manifolds Without Potential Theory Cobo: A Classicallnvitation to Algebraic Numbers and Class Fields Curtis: Abstract Linear Algebra Curtis: Matrix Groups DiBenedetto: Degenerate Parabolic Equations Dimca: Singularities and Topology ofHypersurfaces Edwards: A Formal Background to Mathematics 1 alb Edwards: A Formal Background to Mathematics II alb Foulds: Graph Theory Applications Friedman: Algebraic Surfaces and Holomorphic Vector Bundles Fubrmann: A Polynomial Approach to Linear Algebra Gardiner: AFirst Course in Group Theory GlrdiogfI'ambour: Algebra for Computer Science Goldblatt: Orthogonality and Spacetime Geometry Gustafson/Rao: Numerical Range: The Field ofValues of Linear Operators and Matrices Habn: Quadratic Algebras, Clifford Aigebras, and Arithmetic Win Groups Holmgren: A First Course in Discrete Dynamical Systems Howe!fan: Non-Abelian Harmonic Analysis: Applications of SL(2, R) Howes: Modem Analysis and Topology Hsieh/Sibuya: Basic Theory ofOrdinary Differential Equations HumilMiller: Second Course in Ordinary Differential Equations HurwitzlKritikos: Lectures on Number Theory Jenoiogs: Modem Geomeuy with Applications JonesIMorrislPearson: Abstract Algebra and Farnous Impossibilities Kanoan/Krueger: Advanced Analysis KeUylMattbews: The Non-Euclidean Hyperbolic Plane Kostrikin: lntroduction to Algebra Lueckiog/Rubel: Complex Analysis: A Functional Analysis Approach MacLaoeIMoerdijk: Sheaves in Geometry and Logic Marcus: Number Fields McCartby: lntroduction to Arithmetical Functions (continued after index)

R. Balakrishnan

K. Ranganathan

A Textbook of Graph Theory With 200 Figures

,

Springer

R. Balakrishnan Department of Mathematics Bharathidasan University TiruchirappaJli Tamil Nadu 620 024 India

Editorial Board (North America): S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA

K. Ranganathan National College Tiruchirappalli Tamil Nadu 620 001 India

F.w. Gehring Mathematics Department East Hali University of Michigan Ann Arbor, MI 48109-1109 USA

K.A. Ribet Department of Mathematics University of California at Berkeley Berkeley, CA 94720-3840 USA

Mathematics Subject C1assification (1991): 05-01. OS