Titles in This Serie s

9 Willia m T. Trotter, Editor, Plana r Graph s 8 Simo n Gindikin, Editor, Mathematica l Method s of Analysis of Biopolymer Sequence s 7 Lyl e A. McGeoch and Daniel D. Sleator, Editors, On-Lin e Algorithms 6 Jaco b E . Goodman , Richar d Pollack , an d Willia m Steiger , Editors , Discret e

and Computational Geometry : Paper s from th e DIMACS Special Year 5 Fran k Hwang, Clyde Monma, and Fred Roberts, Editors , Reliabilit y o f Compute r an d

Communication Network s 4 Pete r Gritzman n an d Bern d Sturmfels , Editors , Applie d Geometr y an d Discret e

Mathematics, The Victor Klee Festschrif t 3 E . M. Clarke and R. P. Kurshan, Editors, Computer-Aide d Verificatio n '9 0 2 Joa n Feigenbaum and Michael Merritt, Editors, Distribute d Computin g and Cryptograph y 1 Willia m Cook and Paul D. Seymour, Editors, Polyhedra l Combinatoric s

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Planar Graph s

DIMACS Series i n Discret e Mathematic s

and Theoretica l Compute r Scienc e

Volume 9

Planar Graph s William T . Trotte r

Editor

NSF Scienc e an d Technolog y Cente r in Discret e Mathematic s an d Theoretica l Compute r Scienc e A consortiu m o f Rutger s University , Princeto n University ,

AT&T Bell Labs , Bellcor e

American Mathematica l Societ y

https://doi.org/10.1090/dimacs/009

This DIMAC S volum e resultin g fro m th e Specia l Yea r o n Grap h Theor y an d Algo -rithms contain s researc h article s an d extende d abstract s fro m participant s a t th e Pla -nar Graph s Worksho p hel d a t DIMAC S fro m Novembe r 18 , 199 1 throug h Novembe r 21, 1991 .

1991 Mathematics Subject Classification. Primar y 05C10 , 05C35 , 05C38, 05C75 , 05C85 .

Library of Congress Cataloging-in-Publication Dat a

Planar graphs/William T . Trotter, editor . p. cm.—(DIMAC S series in discrete mathematics and theoretica l compute r science;

v. 9) "Research article s and extended abstract s of participants a t the Planar Graphs Worksho p

held at DIMACS from Novembe r 18 , 1991 through November 21 , 1991"—Fwd. Includes bibliographical references . ISBN 0-8218-6600- 1 1. Graph theory—Congresses . I . Trotter, William T. II . Series.

QA166.P56 199 3 93-2233 9 511/.5-dc20 CI P

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Republication, systemati c copying , o r multipl e reproductio n o f an y materia l i n thi s pub-lication (includin g abstracts) i s permitted onl y under license from th e American Mathematica l Society. Request s for such permission should be addressed to the Manager of Editorial Services, American Mathematica l Society , P.O. Box 6248, Providence, Rhode Island 02940-6248 .

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10 9 8 7 6 5 4 3 2 1 9 8 97 96 95 94 93

Contents

Foreword i x

Preface x i

Cycles, Cocycle s an d Diagonals : A Characterizatio n o f Plana r Graph s DAN ARCHDEACON , C . P . BONNINGTO N AN D C . H . C . LITTL E 1

Stack an d Queu e Layout s o f Directed Plana r Graph s LENWOOD S . HEATH , SRIRA M V . PEMMARAJ U AN D

ANN TREN K 5

Enumeration o f Degree Restricte d Roote d Map s o n th e Spher e E. A . BENDE R AN D E . R . CANFIEL D 1 3

A Generalisatio n o f MacLane' s Theore m t o 3-graph s C. PAU L BONNINGTO N AN D CHARLE S H . C . LITTL E 1 7

Chordal Completion s o f Grid s an d Plana r Graph s F. R . K . CHUN G AN D DAVI D MUMFOR D 3 7

Upward Plana r Drawin g o f Singl e Sourc e Acycli c Digraph s MICHAEL D . HUTTO N AN D ANN A LUBI W 4 1

Flow i n Plana r Graphs : A Survey o f Result s SAMIR KHULLE R AN D JOSEP H (SEFFI ) NAO R 5 9

Planar Grap h Colorin g wit h a n Uncooperativ e Partne r H. A . KlERSTEA D AN D W . T . TROTTE R 8 5

Partitioning a Rectangl e int o Man y Sub-rectangle s so that a Line ca n Mee t onl y a Fe w

DANIEL J . KLEITMA N 9 5

Disjoint Essentia l Circuit s i n Toroida l Map s BOJAN MOHA R AN D NEI L ROBERTSO N 10 9

viii TABL E O F CONTENT S

Layout o f Rooted Tree s JANOS PAC H AN D JEN O TOROCSI K 13 1

Vertex Degree s i n Plana r Graph s

DOUGLAS B . W E S T AN D T O D D WIL L 13 9

List o f Participant s 151

Foreword

This DIMAC S volum e resultin g fro m th e Specia l Year o n Grap h Theor y an d Algorithms contain s researc h article s an d extende d abstract s o f participant s a t the Plana r Graph s Workshop held a t DIMAC S from Novembe r 18 , 1991 through November 21 , 1991. We especially than k th e Worksho p organizer , To m Trotter , for organizin g a n activit y tha t brough t togethe r s o man y outstandin g speaker s and participant s dealin g wit h thi s importan t field.

Fred Roberts , Actin g Directo r

Robert Tarjan , Co-Directo r

Diane Souvaine , Associat e Directo r

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Preface

During th e 1991/9 2 academi c year , Fa n R . K . Chun g an d I serve d a s Co -Directors of the Specia l Year on Graph Theor y an d Algorithm s sponsore d b y th e Center fo r Discret e Mathematics an d Theoretica l Compute r Scienc e (DIMACS) . Based o n informa l feedbac k fro m som e o f th e mor e tha n 30 0 researcher s wh o traveled t o Ne w Jerse y thi s pas t yea r t o participat e i n DIMAC S activities , th e Special Yea r wa s a grea t success . Thi s admittedl y biase d vie w i s supporte d by th e growin g lis t o f accomplishment s i n whic h researcher s recogniz e th e rol e played b y DIMAC S i n initiating , fosterin g an d facilitatin g thei r work .

The Specia l Year o n Grap h Theor y an d Algorithm s feature d fou r workshops :

• Rando m Graph s an d Randomize d Algorithm s Milena Mihai l Joel Spence r

• Plana r Graphs : Structure s an d Algorithm s Tom Trotte r

• Grap h Embedding s an d Paralle l Architecture s Tom Leighto n Bruce Magg s Amy Rosenber g

• Expande r graphs : Theor y an d Application s Persi Diaconi s Joel Friedma n

This monograp h consist s o f researc h article s an d extende d abstract s submit -ted b y participant s i n th e Worksho p o n Plana r Graphs . Mor e tha n 7 0 person s attended thi s Workshop, an d thes e papers cove r a wide range of topics including : enumeration, characterizatio n problems , algorithms , extremal problems, networ k flows and geometry .

I would lik e to expres s m y appreciatio n t o th e person s wh o attende d th e Pla -nar Graph s Worksho p an d contribute d t o it s success . Also , specia l thank s t o the author s o f the article s appearing i n this volume an d t o the man y anonymou s

XI

X l l PREFACE

referees fo r thei r assistanc e wit h th e compositio n o f a volum e whic h wil l (hope -fully) hav e lasting scientific value . Finally , thanks to Christine Thivierge , Donn a Harmon an d Nanc y Gerst l fo r thei r editoria l an d secretaria l assistance .

Tom Trotte r

Director, Combinatoric s an d Optimizatio n Bell Communication s Researc h

Regents Professo r Arizona Stat e Universit y

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List o f

Mike Albertso n Noga Alo n Dan Archdeaco n Jorgen Bang-Jense n Lowell Beinek e Dan Bienstoc k Endre Boro s Rod Canfiel d Guantao Che n Kiran Chilakamarr i Peter Christophe r Marek Chroba k Fan R . K . Chun g Vasek Chvata l Nate Dea n Guoli Din g Dwight Duffu s Genghua Fa n Martin Farac h Mike Fellow s Zoltan Fiired i Ron Graha m Jerry Grigg s Ruth Haa s Glenn Hurlber t David Johnso n Jeff Kah n Howard Karlof f Mark Kayl l

Participants

albertson@smith.smith.edu

noga@math.tau.ac.il archdeac@uvm-gen.uvm.edu jbj@imada.ou.dk beineke@cvax.ipfw.indiana.edu dano@cunixb.cc.columbia.edu boros@ trump. rut gers. edu erc@pollux.cs.uga.edu gchen@plains. nodak. edu kiran@cesvxa.ces. edu

peterrc@wpi.wpi.edu marek@ucrmath.ucr.edu frkc@bellcore.com chvatal@cs.rutgers.edu nate@bellcore.com ding@marais.math.lsu.edu

dwight@mathcs.emory.edu atfan@asuacad.bitnet farach@dimacs. rut gers. edu

mfellows@csr.uvic.ca zoltan@symcom.math.uiuc.edu rlg@research.att. com griggs@math.scarolina.edu rhaas@smith.smith.edu hurlbert@calvin.la.asu.edu dsj@research.att.com jkahn@math.rutgers.edu howard@cc.gatech.edu kayll@math.rutgers.edu

151

152 LIST O F PARTICIPANT S

Suh-Ryung Ki m Daniel J . Kleitma n Tom Leighto n Charles Littl e Anna Lubi w Joe Malkevitc h Gary Mille r Bohan Moha r Seffi Nao r Jarik Nesetfi l Laszlo Pybe r Vijaya Ramachandra n Bruce Ree d Fred Robert s Neil Robertso n Bruce Rothschil d Mike Sak s Ed Scheinerma n Dick Schel p Walter Schnyde r Lex Schrijve r Paul Seymou r Greg Shanno n Alistair Sinclai r Diane Souvain e Gabor Tardo s Bob Tarja n Prasad Tetal i Robin Thoma s Ann Tren k Tom Trotte r Dirk Vertiga n Chi Wan g Doug Wes t Gill Williamso n Peter Winkle r C. Q . Zhan g

kims@sjuvm.bitnet djk@math.mit.edu ftl@math.mit.edu C.little@massey.ac.nz alubiw@maytag.waterloo.edu joeyc@cunyvm.cuny.edu glmiller-h@abacus.theory.cs.cmu.edu bojan.mohar@uni-lj .ac.mail.s i naor@cs.technion.ac.il nesetril@cspugl 1 .bit net hll30pyb@ella.hu

vlr@cs.utexas.edu breed@muff. cs. mcgill. ca frobert s@dimacs. rut gers. edu robertso@function.mps.ohio-state blr@math.ucla.edu saks@math.rutgers.edu ers@cs.jhu.edu schelpr @hermes. msci. memst. edu wschny der @eagle. wesleyan. edu lex@cwi.nl pds@bellcore. com shannon@luap. cs. indiana. edu sinclair@icsi .berkeley. edu dls@cs.rutgers.edu h679tar@ella.hu ret @pr incet on. edu prasad@research.att.com thomas@math.gatech.edu atrenk@lucy.wellesley.edu

wt t @bellcore. com vert igan@dimacs. rut gers. edu cOwang01@ulkyvx.bitner

west@uiucmath.math.uiuc.edu gwilliamson@odin.ucsd.edu pw@bellcore. com cqzhang@wvnvm. wvnet .edu

2014-11-20T13:29:58+0530Preflight Ticket Signature