Vertex-cover in random graphs with small connectivity: an exact solution

TL;DR

This paper discusses the vertex-cover problem in random graphs with small connectivity, but its main results are already known from previous research, leading to its withdrawal.

Contribution

The paper's main findings were previously obtained in other works, and it provides an exact solution for vertex-cover in specific graph models.

Findings

Main result already known from prior work

Exact formula for minimal vertex-cover in trees

Results applicable for c < e in random graphs

Abstract

This paper has been withdrawn by the author, due to the fact that the main result in it has already been obtained in [1] for any c < e, see also [2] and [3]. Moreover the formula which gives the minimal vertex-cover in a tree (see the abstract) has already been derived in [4]. I thank M. Bauer, O. Golinelli, F. Ricci-Tersenghi, G. Semerjian and M. Weigt for having brought to my attention [1] and M.B. and O.G. for [4]. [1] M. Bauer and O. Golinelli, Eur. Phys. J. B 24, 339-352 (2001); [2] R. M. Karp and M. Sipser, Proc. 22nd IEEE Symposium on Foundations of Computing,(1981), 364-375; [3] J. Aronson, A. Frieze, and B.G. Pittel, Random Structures and Algorithms 12 (1998) 111-177; [4] M. Bauer, O. Golinelli, Journal of Integer Sequences, Vol 3, (2000).