Joints in graphs
نویسندگان
چکیده
منابع مشابه
Large joints in graphs
We show that if r s 2; n > r8; and G is a graph of order n containing as many r-cliques as the r-partite Turán graph of order n; then G has more than nr 1=r2r+12 cliques sharing a common edge unless G is isomorphic to the r-partite Turán graph of order n. This structural result generalizes a previous result that has been useful in extremal graph theory.
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In 1969 Erd1⁄2os proved that if r 2 and n > n0 (r) ; every graph G of order n and e (G) > tr (n) has an edge that is contained in at least nr 1= (10r) 6r cliques of order (r + 1) : In this note we improve this bound to nr 1=rr+5: We also prove a corresponding stability result.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.03.045