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EUROPEAN JOURNAL OF COMBINATORICS Editors-in-Chief Patrice Ossona de Mendez Pierre Rosenstiehl Centre d’Analyse et de Math´ ematique Sociales Centre d’Analyse et de Math´ ematique Sociales 190 avenue de France 190 avenue de France 75244 Paris cedex 13 75244 Paris cedex 13 France France Founding Editors Michel Deza, Michel Las Vergnas & Pierre Rosenstiehl Managing Editor ´ Eric Colin de Verdi` ere EDITORIAL BOARD A. Bj ¨ orner Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden B. Bollob ´ as Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 OWB, UK Department of Mathematics, University of Memphis, Campus Box 526429, Memphis, TN 38152-6460, USA F. Brenti Dipartimento di Matematica, Universit´ a di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy A. E. Brouwer University of Technology, Den Dolech 2, PO Box 513, 5600 MB Eindhoven, The Netherlands P. J. Cameron Queen Mary College, London E1 4NS, UK R. Cordovil Department of Mathematics, Instituto Superior ecnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal D. Foata 1, rue Murner, F-67000 Strasbourg P. Frankl 3-12-12 Shibuya, Shibuya-ku, Tokyo, 150-0002, Japan K. Fukuda IFOR, ETH Zentrum, CH-8092 Zurich, Switzerland R. L. Graham Computer Science and Engineering Department, APM 4161 UCSD, 9500 Gilman Drive Dept. 0114, La Jolla, CA, 92093-0404, USA A. A. Ivanov Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, UK G. O. H. Katona Alfr´ ed R´ enyi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Re´ altanoda u. 13-15, Hungary S. Klavˇ zar Department of Mathematics, University of Ljubljana, Jadranska 19 SI-1000 Ljubljana, Slovenia D. Kr´ al’ Mathematics Institute and Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK C. Krattenthaler Fakult¨ at f ¨ ur Mathematik, Universit¨ at Wien, Nordbergstraße 15, A-1090 Vienna, Austria M. Krivelevich Department of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel L. Lov´ asz Microsoft Research 1 Microsoft Way, Redmond, Washington 98052-6399, USA A. Lubotzky Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel A. Mach` ı Dipartimento di Mathematica, Universit` a degli Studi di Roma “La Sapienza”, P le . Aldo Moro, 2, 00185 Roma, Italy J. Neˇ setˇ ril Department of Applied Mathematics and Institute of Theoretical Computer Science, Charles University, Malostransk´ e n´ am 25, 11800 Praha, Czech Republic A. Pasini University of Siena, Via del Capitano 15, 1-53100, Siena, Italy G.N. S ´ ark¨ ozy Department of Computer Science, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA N. M. Singhi TATA Institute for Fundamental Research, Colaba, Bombay 40005, India R. P. Stanley Massachusetts Institute of Technology, Cambridge, MA 02139, USA R. E. Tarjan Princeton University, Princeton, NJ 08544, USA C. Thomassen The Technical University of Denmark, Building 303, DK-2800 Lyngby (Copenhagen), Denmark J. Tits Coll` ege de France, 11 place Marcelin Berthelot, 75005 Paris, France Xuding Zhu Department of Mathematics, Zhejiang Normal University, 688 Yingbin Avenue, Jinhua City, Zhejiang Province, 321004, P.R. China Ce Journal a ´ et´ e pr´ epar´ e avec l’aide administrative de l’ ´ Ecole des Hautes ´ Etudes en Sciences Sociales, de l’Ecole Normale Sup´ erieure de Paris et du Centre National de la Recherche Scientifique. Publication information: European Journal of Combinatorics (ISSN 0195-6698). For 2014, volumes 35 to 42 are scheduled for publication. Subscription prices are available upon request from the Publisher or from the Elsevier Customer Service Department nearest you or from this journal’s website (http://www.elsevier.com/locate/ejc). Further information is available on this journal and other Elsevier products through Elsevier’s website (http://www.elsevier.com). Subscriptions are accepted on a prepaid basis only and are entered on a calendar year basis. Issues are sent by standard mail (surface within Europe, air delivery outside Europe). Priority rates are available upon request. Claims for missing issues should be made within six months of the date of dispatch.

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EUROPEAN JOURNAL OF COMBINATORICSEditors-in-Chief

Patrice Ossona de Mendez Pierre RosenstiehlCentre d’Analyse et de Mathematique Sociales Centre d’Analyse et de Mathematique Sociales

190 avenue de France 190 avenue de France75244 Paris cedex 13 75244 Paris cedex 13

France France

Founding Editors

Michel Deza, Michel Las Vergnas & Pierre Rosenstiehl

Managing Editor

Eric Colin de Verdiere

EDITORIAL BOARDA. BjornerDepartment of Mathematics, Royal Institute ofTechnology, S-10044 Stockholm, SwedenB. BollobasDepartment of Pure Mathematics and Mathematical Statistics,University of Cambridge, Wilberforce Road,Cambridge CB3 OWB, UKDepartment of Mathematics, University of Memphis,Campus Box 526429, Memphis, TN 38152-6460, USAF. BrentiDipartimento di Matematica, Universita di Roma“Tor Vergata”, Via della Ricerca Scientifica 1,00133 Roma, ItalyA. E. BrouwerUniversity of Technology, Den Dolech 2,PO Box 513, 5600 MB Eindhoven, The NetherlandsP. J. CameronQueen Mary College, London E1 4NS, UKR. CordovilDepartment of Mathematics, Instituto SuperiorTecnico, Av. Rovisco Pais, 1096 Lisboa Codex, PortugalD. Foata1, rue Murner,F-67000 StrasbourgP. Frankl3-12-12 Shibuya, Shibuya-ku, Tokyo, 150-0002, JapanK. FukudaIFOR, ETH Zentrum,CH-8092 Zurich, SwitzerlandR. L. GrahamComputer Science and Engineering Department,APM 4161 UCSD, 9500 Gilman Drive Dept. 0114,La Jolla, CA, 92093-0404, USAA. A. IvanovDepartment of Mathematics, Imperial College,180 Queen’s Gate, London SW7 2BZ, UKG. O. H. KatonaAlfred Renyi Institute of Mathematics,Hungarian Academy of Sciences, H-1053 Budapest,Realtanoda u. 13-15, HungaryS. KlavzarDepartment of Mathematics, University of Ljubljana,Jadranska 19 SI-1000 Ljubljana, SloveniaD. Kral’Mathematics Institute and Department of Computer Science,University of Warwick, Coventry, CV4 7AL, UK

C. KrattenthalerFakultat fur Mathematik, Universitat Wien,Nordbergstraße 15, A-1090 Vienna, AustriaM. KrivelevichDepartment of Mathematics, Tel Aviv University,Tel Aviv 69978, IsraelL. LovaszMicrosoft Research 1 Microsoft Way,Redmond, Washington 98052-6399, USAA. LubotzkyInstitute of Mathematics, Hebrew University,Jerusalem 91904, IsraelA. MachıDipartimento di Mathematica, Universita degliStudi di Roma “La Sapienza”, P le. Aldo Moro, 2,00185 Roma, ItalyJ. NesetrilDepartment of Applied Mathematics and Instituteof Theoretical Computer Science,Charles University, Malostranske nam 25,11800 Praha, Czech RepublicA. PasiniUniversity of Siena, Via del Capitano 15, 1-53100,Siena, ItalyG.N. SarkozyDepartment of Computer Science, Worcester PolytechnicInstitute, 100 Institute Road, Worcester, MA 01609, USAN. M. SinghiTATA Institute for Fundamental Research,Colaba, Bombay 40005, IndiaR. P. StanleyMassachusetts Institute of Technology, Cambridge,MA 02139, USAR. E. TarjanPrinceton University, Princeton, NJ 08544, USAC. ThomassenThe Technical University of Denmark, Building303, DK-2800 Lyngby (Copenhagen), DenmarkJ. TitsCollege de France, 11 place Marcelin Berthelot,75005 Paris, FranceXuding ZhuDepartment of Mathematics, Zhejiang Normal University,688 Yingbin Avenue, Jinhua City,Zhejiang Province, 321004, P.R. China

Ce Journal a ete prepare avec l’aide administrative de l’Ecole des Hautes Etudes en Sciences Sociales, de l’Ecole Normale Superieurede Paris et du Centre National de la Recherche Scientifique.

Publication information: European Journal of Combinatorics (ISSN 0195-6698). For 2014, volumes 35 to 42 are scheduled forpublication. Subscription prices are available upon request from the Publisher or from the Elsevier Customer Service Departmentnearest you or from this journal’s website (http://www.elsevier.com/locate/ejc). Further information is available on this journal andother Elsevier products through Elsevier’s website (http://www.elsevier.com). Subscriptions are accepted on a prepaid basis only andare entered on a calendar year basis. Issues are sent by standard mail (surface within Europe, air delivery outside Europe). Priorityrates are available upon request. Claims for missing issues should be made within six months of the date of dispatch.