### Abstract

Denote by G(n; m) a graph of n vertices and m edges. We prove that every G(n; [n^{2}/4]+1) contains a circuit of l edges for every 3 ≦l2n, also that every G(n; [n^{2}/4]+1) contains a k_{e}(u_{n}, u_{n}) with u_{n}=[c_{1} log n] (for the definition of k_{e}(u_{n}, u_{n}) see the introduction). Finally for t>t_{0} every G(n; [tn^{3/2}]) contains a circuit of 2 l edges for 2≦l3t^{2}.

Original language | English |
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Pages (from-to) | 156-160 |

Number of pages | 5 |

Journal | Israel Journal of Mathematics |

Volume | 1 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1963 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*1*(3), 156-160. https://doi.org/10.1007/BF02759702

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

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 1, no. 3, pp. 156-160. https://doi.org/10.1007/BF02759702

}

TY - JOUR

T1 - On the structure of linear graphs

AU - Erdős, P.

PY - 1963/9

Y1 - 1963/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=51249161756&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249161756&partnerID=8YFLogxK

U2 - 10.1007/BF02759702

DO - 10.1007/BF02759702

M3 - Article

AN - SCOPUS:51249161756

VL - 1

SP - 156

EP - 160

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 3

ER -