An Extremal Problem On Ksubr Free Graphs

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An Extremal Problem On Ksubr Free Graphs
Peter Frankl
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, x, } CV, let T{{xi, X2, ■ ■ ■, x, ]) be the number of vertices joined to all x^ (l j:ViVjiE(G') " " J-. ViVjiEiC) 1-i where the last inequality follows by (1) and (2). Thus there exists a specific t-tuple {j:i, ;c2, . . . , x, ] CV, such that 1-- 2 y(5(V„V;))'(1-€ ^)^T{{x„. . . , x, })^cn j:ViVjiE(. G') whence 2. 3 follows immediately. □ Since any edge of G connects (a) either two classes (V, Vj) such that V, Vj€£:(G'), (b) or an e-irregular pair (V, V^), (c) or a pair (V, V;) with 8(V, V;) £... €''+€, (d) or two points belonging to the same class V, we obtain |£(G)| |£(G*)1 rs6(VMV;)V I |£(G*)1 r [(|£(G) |£(G')|'-i LVi , _3A=, %.

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