# On the structure of linear graphs

Article

- Received:

DOI: 10.1007/BF02759702

- Cite this article as:
- Erdös, P. Israel J. Math. (1963) 1: 156. doi:10.1007/BF02759702

- 19 Citations
- 65 Views

## 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 ≦*l*<*c*_{2}*n*, 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≦*l*<*c*_{3}*t*^{2}.

## Copyright information

© Hebrew University 1963