Induced trees in sparse random graphs

The random graphG(n, p) onn vertices with edge probabilityp = c/n contains an induced tree of orderαcn whereαc > 0 forc > 1. This proves a conjecture of Erdös and Palka.

[1]  Marco Protasi,et al.  The Largest Tree in a Random Graph , 1983, Theor. Comput. Sci..

[2]  T. Kurtz.  Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[3]  B. Bollobás.  The evolution of random graphs , 1984 .

[4]  Paul Erdös,et al.  Trees in random graphs , 1983, Discret. Math..

[5]  Richard M. Karp,et al.  Maximum Matchings in Sparse Random Graphs , 1981, FOCS 1981.

[6]  M. Sipser,et al.  Maximum matching in sparse random graphs , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[7]  János Komlós,et al.  The longest path in a random graph , 1981, Comb..