Table Of Content

Glossary of Notation ‘Nan-alphabetie notation u wa asipooney rion oreese alton tera Sermo ato ‘sigramcee satin Tepteston Date aber cling af buurber i bass eae af erber Be feet Bet desorption inaaier abet oben bernie ey complet of eaph or 90 paver nl Epower of raph set ot apes for & Etktional vero Ekin aed Salsa ode discat unde oP yan inal erapie Casta peedast gia ‘pues dilrence trun duplicates eres yall: castedian peiduce ste ‘igerouceofeate enon neicene ‘ional arian rent Roman alphabet wiles 2 diane deca bu za we audi ‘ea of aso seca aad Sele wich seriers power ofa ere Eber of eonente ‘Glaadleriaa ehoone Soave seavenee dosree of eres turcdecee, depts ieee (Esteace eat. flseaace er 0 thacoeee Aetarmnast fae s2r ‘xpecod valua Eom mer of eget tora atic to tol eatating oe funeiva, es vce ese trap for ies ‘auido graph in Noel A Hovaiy soap, independent sats of watesid idesity aie ‘isin ali feonsieto work fomsletebivarticegronh Tne geoph Iver bora ou dow ni eu Introduction to Graph Theory Second Edition Douglas B. West University of Minois — Urbana ‘outer and publister ois book hve used ear beset a preparing stock, bee effets inelode te devslpoce, esetc, and sting othe theories abd poy te dense Bhar ‘ftctveness. The abr an publisher make 0 waren of apy ind expressed or Spied. wit egad © These prams ore documentation sonnei thi how Thonn aed pes sall at hs ils sy evar fer neidenal ar eansoquential damage in connection With, or arising etc, the unin, petfommunce, ruse of thewe prim, Copaigh 9 2001 by Pearson Eduction. ne This editin is polished by steangetcor wih Pearson Busan, Ie. All ght sosrvo. No pat af this plication may be rpradace, sored in a datase or revel aystom, bemaniaite i any frm by au means, lecroic, mesbunicl photocupyeng.reverdng, OF beri, ‘without ie prior ee pais othe publish (SUN #1-7606-850-4 irs nin Reprint, 2002 This edtion is manafacrred in tndia end is authored far sale only i india, Bangladesh, Pakistan, Nepal St anke aad ihe Molds. Published by Pessoa Fdoaton(Sioaptns) Pe La edi: Brabe, 482 FI.B. Paar ela 110092, India Print in Toa by Rass Pri, For my dear wife Ching and for all lovers of graph theory Contents Preface Chapter 1 Fundamental Concepts La What Is u Graph? ‘The Definition, L draphe aa Models, 3 ‘Matrices and leamorphiera, Decompositio and Special Graphs, 11 xereicen, 11 12. Paths, Cycles, and Trails Connection ia Geapha, 20 Ripartite raphe, 24 Rolesian Cireuite, 26 Bzereieen 18. Vertex Degrees and Counting Counting nd Bijetions, $5 Extremal Probluns, 38 Gruphie Sequences. 44 Bxereisus, 47 LA. Ditweted Graphe Definitions and Example, 88 Vertex Degrees, 58 Bolerin Digraphs, 60 Orientations snd Towranments, 61 Reereiacs, 69 1” ry Chapter 2 Trees and Distance 2.1 Basic Properties Proparties of Tress, 8 Diztanee in Treea aad Graphs 10 Digjoint Spanning Tress optional, 19 Exercises, 75 2.2 Snenning Trees and Eywmeration Enumeration of Trees, 81 Spanning Trees in Graphs, 84 Decempesitios and Gracefol Labelings, 87 Branchings and Gulerian Digraphs (optional), 89 Exercices, 92 23 Optimisation and Trees ‘Minimom Spamning Tree, 95 Shortest Patha, 97 ‘Troea in Computer Seience (optional), 100 Exereices, 103 Chapter 3. Matchings and Factors 84. Matching am Covers Maxdunun Matehings, 108 ‘ifs Matebing Condition, 110 ‘Minv-Max Theorema, 112 Independent Sete and Covers, 113, Daminating Seta options), 116 LExercices, La $2 Algorithme ond Applications Maximum Bipartte Macching, 23 Vieighted Bipartite Macching, 12 Stable Matehings copeianal, 130 Paster Biparcce Matching optional, 182 Exercines, UP 83 Matching in General Graphs ‘Tater's (factor Thoorem, 138 {f-facors of Gruphs foptionaD, 140 Edmond’ Blnasom Algoritm (aptivnaD, 142 Exveioes, WR Contents er “ a 107 sor 123 16 Cameos Chapter 4 Connectivity and Paths 43 Cuts and Comnectivity Connectivity, 49 Falge-ennasctivity, 15 Becks, 155 Bereines 158 42 ioonnected Graphs connected Craps, 181 Comectivity of Digrapha, 164 ‘connected and tedge-connested Crapha, 166 “Applicatios of Menger’s Theorem, 170, Bxercices, 172 44 Network Flow Probleme Maximum Network Flow, 176 Integrat flows, 181 Supplies and Demanda (optional), 14 Exercises, 168 Chapter 5 Coloring of Graphs 5. Vertex Colorings and Upper Bounds Definitions and Examples, 191 Upper Bounds, 194 Broclo’ Theozem, 197 Bxerelacs, 169 52 Structure of chromatic Graphs raphe with Tasge Chremutie Nornbor, 205 [Extzemal Probleme and Turéw's Theorem 207 Color-Critie Graph, 210 Forel Subdivisions, 242 Bexerieos, 214 58 Baumerntive Aspects Counting Proper Coltings 218 Chordat Graphs, 225 A Fit of ecteet Grupa, 228, Counting Acyclic Orientacivne optiuna, 228 Bxercines, 220 149 181 176 1st 101 aie Chapter 6 Planar Graphs 61 Embodillngs and Euler's Formola Drawings in the Plane, 293 Dual Graphs, 238 Boter’s Formal, 241 255 Brereisos, 248 G2 Characterization of Planar Grapha Preparation lor Kurstawas Theorem, 247 Convex Embeddings, 248 Flimorlty Testing CoptionaD, 252 Bxerciees, 257 63 Parameters of Planarity Coloring of Planar Grapha, 257 Ceoasing Nuber, 261 Surfaces of ligher Genus xereises, 209 optional, 166 Chapter 7 Edges and Cycles 714. Line Graphs and Edgevoloring Lage-colaringa, 274 Characterization of Line Graphs (optional), 279 Exercises, 282 72 Hamiltonian Cycler [Necessary Conditions. 283 Sufleiont Conditions, 288 Cycles in Dizosted Graphs Copious). 288 Excreivos, 294 13 Plonarity, Coloring, and Cycle ‘Tait Theorom, 200 Grinberg These, 302 Barks optional, 304 lowe and Cycle Cavers (optional, $07 Exercines, 314 288 283 M6 257 273 am Contunee ie Chapter 8 Additional Topics (optional) m9 84. Perfect Graphs ae ‘The Poet Graph Theorem, 920 Choral Grapha Revisited, #28 Other Classes of Porter Geaphs, 928 Imperfect Graphs, ‘The Htrong Perfect Graph Conjee Bxereisen, 204 82 Mufrolds ae Hereditary Systeme and Examples, S48 Propurtiod of Malroids, $54 ‘The Spon Funecion, 858 ‘The Dual ofa Mauro 860 Macenid Minavs and Planar Graph, 968 Matra Intersection, 348 Matreid Unions 269, xercizes, 372 88 Ramsey Theory ate ‘Tho Piquaahole Frlusiple Revisited, S78 Ruorsey Thosren, 360 Romsey Nueabers, 288 heaph Raney They 386 Sperser's lama soul Bundwidth, 988 Bxerceey, 392 84 More Extremal Probleme 396 Browdings of Graphs, 387 Branchings und Gossip, 404 Last Coloring und Choovability, 408 Porttions Using Pathe andl Crees, 415 Gireumferenes, 418, Bxerenes, 2 85 Random Graphs 98 Bxistonce and Expectation, 426, Properties of Almost All Graphs, 420 ‘Threshold Funevona, 432 Evolution ond Gruph Parameters, £26 Connectivity, Cliquss, and Coloring, 438 Moartingoles, 442 Bacreisns, 448