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 ≦l2n, 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≦l3t2.

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

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Cite this

On the structure of linear graphs. / Erdős, P.

In: Israel Journal of Mathematics, Vol. 1, No. 3, 09.1963, p. 156-160.

Research output: Contribution to journalArticle

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