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Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) n 2 wi ..."
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) n 2 with 0 < α < 17 −3 (), and G has no book of size at least graph G1 of order at least
THE SIZE OF CHORDAL, INTERVAL AND THRESHOLD SUBGRAPHS
 COMBINATORICA 9(3)(1989)245253
, 1989
"... Given a graph G with II vertices and m edges, how many edges must be in thelargest chordal subgraph of G? For m=na/4+ 1, the answer is 3n/2 1. For m=na/3, it is 2n3. For m = n2/3 + 1, it is at least 7n/3 6 and at most 8n/3 4. Similar questions are studied, with less complete resuIts, for thresho ..."
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Cited by 1 (0 self)
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Given a graph G with II vertices and m edges, how many edges must be in thelargest chordal subgraph of G? For m=na/4+ 1, the answer is 3n/2 1. For m=na/3, it is 2n3. For m = n2/3 + 1, it is at least 7n/3 6 and at most 8n/3 4. Similar questions are studied, with less complete resuIts, for threshold graphs, interval graphs, and the stars on edges, triangles, and &‘s.