On the structure of linear graphs

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Abstract

Denote by G(n; m) a graph of n vertices and m edges. We prove that every G(n; [n2/4]+1) contains a circuit of l edges for every 3 ≦l<c2n, also that every G(n; [n2/4]+1) contains a ke(un, un) with un=[c1 log n] (for the definition of ke(un, un) see the introduction). Finally for t>t0 every G(n; [tn3/2]) contains a circuit of 2 l edges for 2≦l<c3t2.

Original languageEnglish
Pages (from-to)156-160
Number of pages5
JournalIsrael Journal of Mathematics
Volume1
Issue number3
DOIs
Publication statusPublished - Sep 1 1963

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ASJC Scopus subject areas

  • Mathematics(all)

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