By Claude Berge C.N.R.S. (auth.), Claude Berge, Dijen Ray-Chaudhuri (eds.)
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Extra resources for Hypergraph Seminar: Ohio State University 1972
Or il existe une unique clique contenant y. : C et d'apr~s le len~ne 4 elle est coupl~e avec i yl,yi disjoinEs etant xlY I et xiYi). P7 Lemme 6. Soit aux ordres n G un graphe simple ygrifiant PI' P2 et h, alors G p eut s'~crire graphe G est formg de G ~, que l'on va construire. D. , P3' P4' pbis 4 ' P5 e__tt xI n un point de ~ i ( G m) d'un une clique maximale contenant copies G et soit x I. n. ,n. yn } Yl (lemme 5). Posons appartient donc ~ l'unique clique coupl~e ~ i(Yl ) = Yi' o~ Yi Dl(Xi)-C.
1 < r < m , 1
3, then 3 5/3 < c"s n ~ ( K n X K s ) -- the lower bounds for the general case are far from the upper bound given in (i).
Follows. Q. E. D. Corollary 3, Let H = ~(H) ~ (H') This Corollary 4, be a hypergraph for every hypergraph follows immediately Let and H H' Furthermore, if Clearly, Thus, Corollary then H if H p(H) p ( H ' ) then is the dual of Then ~(HxH') Then : p(HxH') H , then : p(H) #(H') for every 0(H) = T(H ) . If H H' o is is also balanced. the result i. • . be two hypergraphs. is balanced, H H' m(H) = *(H) 6(H) from Lemma Io p(HxU')< balanced, such that follows immediately from Proposition i, Proposition 2 and = 28 Corollary 5.
Hypergraph Seminar: Ohio State University 1972 by Claude Berge C.N.R.S. (auth.), Claude Berge, Dijen Ray-Chaudhuri (eds.)