Abstract
We propose a problem concerning the determination of the threshold function for the edge probability that guarantees, almost surely, the existence of various sparse spanning subgraphs in random graphs. We prove some bounds and demonstrate them in the cases of ad-cube and a two dimensional lattice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bollobás B: Random Graphs. New York: Academic Press, 1985
McDiarmid C., Miller Z.: Lattice bandwidth of random graphs. Discrete App. Math.30 221–227 (1991)
Erdös P., Szemerédi E.: Some recent combinatorial problems, preprint, 1990.
Hajnal A., Szemerédi E.: Proof of a conjecture of Erdös. In: Combinatorial Theory and its Applications, Vol. II (P. Erdös, A. Renyi and V.T. Sós eds.), Colloq. Math. Soc. J. Bolyai 4. (1970) pp. 601–623. Amsterdam: North Holland
Venkatesan R., Levin L.: Random instances of a graph coloring problem are hard. In: Proc. of the 20th AnnualSTOC, ACM Press. pp. 217–222 (1988)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alon, N., Füredi, Z. Spanning subgraphs of random graphs. Graphs and Combinatorics 8, 91–94 (1992). https://doi.org/10.1007/BF01271712
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01271712