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On the structure of linear graphs

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Abstract

Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n 2/4]+1) contains a circuit ofl edges for every 3 ≦l<c 2 n, also that everyG(n; [n 2/4]+1) contains ak e(u n, un) withu n=[c 1 logn] (for the definition ofk e(u n, un) see the introduction). Finally fort>t 0 everyG(n; [tn 3/2]) contains a circuit of 2l edges for 2≦l<c 3 t 2.

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Authors and Affiliations

  1. University of Michigan, Ann Arbor, Michigan, U.S.A.

    P. Erdös

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  1. P. Erdös
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Additional information

This work was done while the author received support from the National Science Foundation, N.S.F. G.88.

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Erdös, P. On the structure of linear graphs. Israel J. Math. 1, 156–160 (1963). https://doi.org/10.1007/BF02759702

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  • DOI: https://doi.org/10.1007/BF02759702

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