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By Claude Berge C.N.R.S. (auth.), Claude Berge, Dijen Ray-Chaudhuri (eds.)

ISBN-10: 3540068465

ISBN-13: 9783540068464

ISBN-10: 3540378030

ISBN-13: 9783540378037

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Pour d~montrer les th~or~mes A e t e--it B nous aurons besoin des d~finitions suivantes. t C' de sommets y ~ C'-C. de C G seront dites coupl~es, et ceux de C', telle qu'un sont adjacents si et seulement s i i l s se correspondent dans la bijection ; deux tels sommets seront dits coupl~s. On peut dire aussi que v~rifiant C U C' = C+K 2 = C'+K 2. (Deux cliques coupl~es sont deux cliques "6(C,C') = 2" Remarquons clans [I] ou "appartenant g que ~oute clique maximale de G ~(G)" dans r~5~). contient n sommets d'apr~s P6 et que deux Cliques coupl~es sont disjointes : en effet s i x ~ C ~ C', il n'y a _bis.

H ~tant un entier positif et nI ! n h ensembles disjoints, Xk, avec I Xkl = n k ; les h sommets de Kh sont les ~l~ments de nl'n2"'nh E i de X, telles que IEi ~ Xkl = I parties bans le cas o~ nk = n pour tout X = Q X k et les armies sont les k pour tout k (I< k< h). k, on notera cet hypergraphe . Ces hypergraphes constituent une g~n~ralisation du graphe biparti complet xn (cas h=2 de la d~finition) D~finition 2. H et sont ~tudi~s dans [3] ~tant un hypergraphe simple, simple, dont les sommets repr~sentent les ar~tes de et [13].

On graphs which do not contain a Thomsen graph, Canad. Math° Bullo 2, 1966, 281-28~. 3. , Hypersraphs and Ramseyian theorems, Thesis, Univo of Waterloo, 1970. 4. , On finite polarized partition relations, Canad. Math. Bull. 12, 1969, 321-326. 5. Culik, Eo, Teilweise Losung eines verallgemeinerten Problems yon Ko Zarankiewicz, Ann. , 1956, 165-168. 6. , and Rado, Ro, A partition calculus in set theory, Bull. S. 62, 1956, 427-489. 7. Guy, R. , A problem of Zarankiewicz in Theory of Graphs, Akad~miai Kiad~, Budapest, 1968, 119-150o 8.

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Hypergraph Seminar: Ohio State University 1972 by Claude Berge C.N.R.S. (auth.), Claude Berge, Dijen Ray-Chaudhuri (eds.)

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