XPrefaceKelmans, Henry Kierstead, Laszlo Lovasz, Claudio Lucchesi, George Purdy, Di-eterRautenbach.BruceReed.BruceRichmond.NeilRobertson.Alexander Schrijver, Paul Seymour, Miklos Simonovits, Balazs Szegedy, Robin Thomas, StephanThommasse, Carsten Thomassen, and Jacques Verstraete. We thank them all warmlyfortheir various contributions. We are grateful also to Martin Crossley for allowingus to use (in Figure 10.24) drawings of the Mobius band and the torus taken fromhis book Crossley (2005).Facilities and support were kindly provided by Maurice Pouzet at UniversiteLyon 1 and Jean Fonlupt at Universite Paris 6. The glossary was prepared usingsoftware designed by Nicola Talbot of the University of East Anglia. Her promptlyoffered adviceappreciated.Finallywebenefittedfromafruitful relationship with Karen Borthwick at Springer,and from the technical help provided byher colleagues Brian Bishop and Frank Ganz.We are dedicating this book to the memory of our friends Claude Berge, PaulErdos, and BilTutteItowes its exstencetotheirachievements, theirguidinghands, and their personal kindness.J.A. Bondy and U.S.R. MurtySeptember 2007X Preface Kelmans, Henry Kierstead, L´aszl´o Lov´asz, Cl´audio Lucchesi, George Purdy, Di￾eter Rautenbach, Bruce Reed, Bruce Richmond, Neil Robertson, Alexander Schri￾jver, Paul Seymour, Mikl´os Simonovits, Balazs Szegedy, Robin Thomas, St´ephan Thomass´e, Carsten Thomassen, and Jacques Verstra¨ete. We thank them all warmly for their various contributions. We are grateful also to Martin Crossley for allowing us to use (in Figure 10.24) drawings of the M¨obius band and the torus taken from his book Crossley (2005). Facilities and support were kindly provided by Maurice Pouzet at Universit´e Lyon 1 and Jean Fonlupt at Universit´e Paris 6. The glossary was prepared using software designed by Nicola Talbot of the University of East Anglia. Her promptly￾offered advice is much appreciated. Finally, we benefitted from a fruitful relation￾ship with Karen Borthwick at Springer, and from the technical help provided by her colleagues Brian Bishop and Frank Ganz. We are dedicating this book to the memory of our friends Claude Berge, Paul Erd˝os, and Bill Tutte. It owes its existence to their achievements, their guiding hands, and their personal kindness. J.A. Bondy and U.S.R. Murty September 2007