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View This Volume's Front and Back Matter Applied Geometr y and Discret e Mathematic s The Victo r Kle e Festschrif t This page intentionally left blank DIMACShttps://doi.org/10.1090/dimacs/004 Series in Discrete Mathematic s and Theoretical Computer Scienc e Volume 4 Applied Geometr y and Discret e Mathematic s The Victo r Kle e Festschrif t Peter Gritzman n Bernd Sturmfel s Editors NSF Scienc e an d Technolog y Cente r in Discret e Mathematic s an d Theoretica l Compute r Scienc e A consortium o f Rutgers University , Princeto n University , AT&T Bell Labs , Bellcor e 198 0 Mathematics Subject Classification (198 5 Revision). Primary 05 , 15 , 28 , 46 , 51 , 52 , 57, 65 , 68 , 90 . Library of Congress Cataloging-in-Publication Data Applie d geometr y an d discret e mathematics : Th e Victo r Kle e festschrift/Pete r Gritzmann , Bern d Sturmfels , editors . p. cm.—(DIMAC S serie s in discret e mathematic s an d theoretica l compute r science , ISS N 1052-1798 ; v. 4) Include s bibliographica l references . AMS : ISB N 0-8218-6593- 5 (acid-fre e paper ) ACM : ISB N 0-89791-385- X (acid-fre e paper ) 1. Mathematics . 2. Klee , Victor . I. Gritzmann , Peter , 1954 - . II. Sturmfels , Bernd , 1962- . III. Klee , Victor . IV . Series . QA7.A66 4 199 1 90-2693 4 510—dc2 0 CI P To orde r throug h AM S contac t the AM S Custome r Service s Department , P.O . Bo x 6248 , Providence , Rhod e Islan d 02940-624 8 USA . Fo r VIS A or MASTERCAR D order s cal l 1-800-321 - 4AMS . Orde r cod e DIMACS/4 . To orde r throug h AC M contac t AC M Orde r Department , P.O . Bo x 64145 , Baltimore , Mary - lan d 21264 . Phon e 301-528-4261 . Orde r numbe r 222912 . Copying and reprinting. Individua l reader s of this publication , an d nonprofi t librarie s actin g for them , ar e permitte d to mak e fai r us e of the material , suc h a s to cop y a n articl e for use in teachin g or research . Permissio n is grante d to quot e brie f passage s from this publicatio n in reviews , provide d the customar y acknowledgmen t of the sourc e is given . Republication , systemati c copying , or multipl e reproductio n of an y materia l in this pub - licatio n (includin g abstracts ) is permitte d onl y unde r licens e from the America n Mathematica l Society . Request s for suc h permissio n shoul d be addresse d to the Manager of Editoria l Ser - vices , America n Mathematica l Society , P.O . Bo x 6248 , Providence , Rhod e Island 02940-6248 . Th e appearanc e of the cod e on the first pag e of a n articl e in this boo k indicate s the copyrigh t owner' s consen t for copyin g beyon d tha t permitte d by Section s 10 7 or 10 8 of the U.S . Copyrigh t Law , provide d tha t the fe e of $1.0 0 plu s $.2 5 pe r pag e for eac h cop y be pai d directl y to the Copyrigh t Clearanc e Center , Inc. , 27 Congres s Street , Salem , Massachusett s 01970 . Thi s consen t doe s no t exten d to othe r kind s of copying , suc h a s copyin g for genera l distribution , for advertisin g or promotiona l purposes , for creatin g ne w collectiv e works , or for resale . Copyright ©1991 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. © This publication was typeset using ^S-TEX, the American Mathematical Society's T^X macro system. 10987654321 959493929 1 Foreword This DIMACS volume, The "Victor Kle e Festschrift," i s a collection o f research and survey papers that are related to the work of Victor Klee. Th e publication o f thi s boo k o n th e occasio n o f Professo r Klee' s 65t h birth - day mirrors the breadth o f his mathematical contributions . W e especially thank th e editors, Peter Gritzmann an d Bern d Sturmfels , fo r preparin g a volume tha t contain s article s o n suc h a variety o f subjects , an d tha t i s a suitable tribute to a leader in the field of discrete mathematics. Daniel Gorenstein, Directo r Robert Tarjan , Co-Directo r Fred S . Roberts, Associate Directo r This page intentionally left blank Brief Contents Preface i x Biography o f Victor Klee x i Bibliography o f Victor Klee xvi i Contents (i n alphabetical order by author) xxx i List o f Papers (b y subjects) xxx v Contributed Article s 1-60 8 This page intentionally left blank Preface This volume comprises a collection of research articles dedicated to Victor Klee on the occasion of his 65th birthday in September 1990 . Al l papers are related t o Victo r Klee' s researc h work , and , i n vie w o f hi s broad interests , a wide range o f area s in mathematics an d it s applications ar e touched upo n here. Thes e areas include • Discrete and Computational Geometry , • Classical and Computational Convexity , • Convex Polytopes and their Relatives, • Combinatorics, Polyhedra l Combinatorics, an d Graph Theory , • Functional Analysis, • Mathematical Programmin g and Optimization, an d • Theoretical Computer Science . Victor Klee has made significant contribution s not only to all of the above fields, bu t als o t o mathematic s education , mathematica l method s i n eco - nomics an d th e decisio n sciences , application s o f discret e mathematic s i n the biological an d socia l sciences , an d informatio n linkag e between applie d mathematics an d industry . Rathe r tha n attemptin g t o summariz e o r com - ment o n Victo r Klee' s numerou s professiona l achievements , w e let hi s vita and bibliography spea k for themselves . Following th e spiri t o f Victo r Klee' s holisti c vie w o f mathematics , th e present collectio n i s no t divide d int o mathematica l subcategories , bu t th e articles appea r i n alphabetica l orde r b y first author . I n orde r t o facilitat e browsing through this volume and to give easy access to papers belonging to the same area, we include a list o f papers by subject area . We are indebted t o the Center fo r Discret e Mathematics an d Theoretica l Computer Science , in particular to its director Daniel Gorenstein, and to the American Mathematica l Societ y fo r thei r hel p i n arrangin g th e publicatio n of this volume. W e wish to thank th e referee s fo r thei r invaluabl e help an d the authors for their enthusiastic support throughout this project. But , above all, w e join al l contributor s i n thei r birthda y wishe s expressin g th e deepes t gratitude to Victor Kle e for al l that h e has given to us. Peter Gritzmann an d Bern d Sturmfel s September 199 0 ix t^p photograph by Lisette Klce — Victor Kle e — Biography of Victor Klee Personal Born in Sa n Francisco, 192 5 Education Ph.D., University o f Virginia, 194 9 B.A., Pomona College , 194 5 Honorary Degree s D.Sc, Universite d e Liege, 198 4 D.Sc, Pomona College , 196 5 Awards Pomona Colleg e David Prescot t Barrow s Award fo r Distinguishe d Achievement , 1988 Reed Colleg e VoUum Award fo r Distinguishe d Accomplishmen t i n Scienc e and Technology, 198 2 Alexander von Humboldt Stiftun g Preistrager, 1980-198 1 Mathematical Associatio n o f Americ a C. B. Allendoerfer Award , 198 0 Annual Award fo r Distinguishe d Servic e to Mathematics, 197 7 L. R. Ford Award , 197 2 University o f Virgini a President's and Vistor's Research Prize, 195 2 Full-time Employmen t University o f Washingto n Professor o f Mathematics, 1957-presen t Associate Professor, 1954-195 7 Assistant Professor , 1953-195 4 xii BIOGRAPH Y O F VICTO R KLE E Adjunct Professo r o f Computer Science , 1974-presen t Professor o r Adjunct Professo r o f Applied Mathematics, 1976-198 4 University o f Western Australi a Visiting Professor, 197 9 University o f Victori a Visiting Professor, 197 5 T. J. Watson Researc h Center , IB M Full-time Consultant, 197 2 University o f Colorad o Visiting Professor, 197 1 University o f California, Lo s Angeles Visiting Associate Professor, 1955-195 6 University o f Virgini a Assistant Professor , 1949-195 3 Instructor, 1947-194 8 Fellowships Senior Fellow, Institute fo r Mathematic s an d its Applications, Min - neapolis, 198 7 Mathematical Science s Research Institute , Berkeley , 1985-198 6 Guggenheim Fellow , University o f Erlangen-Nurnberg, 1980-198 1 Center fo r Advance d Stud y in the Behavioral Sciences , Stanford, 1975 - 1976 Sloan Foundation Fellow , University o f Copenhagen, 1959-196 0 National Scienc e Foundation Senio r Postdoctoral Fellow , Universit y of Copenhagen , 1958-195 9 Research Fello w of the Alfred P .
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