On large induced trees and long induced paths in sparse random graphs

6Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

Let Gn,p denote the graph obtained from deleting the edges of Kn, the complete graph with vertex set Vn = {1,2, ..., n}, independently with equal probability 1 - p. Assume that p = p(n) is such that np = c > 1. We describe an algorithm FindTree for finding induced trees in a graph. By analyzing how FindTree performs in Gn,p, we obtain the following results. Let Tn be the order of the largest induced subtree of Gn,p. We find a number t(c) such that Tn is almost surely larger than (t(c) - ε)n for any ε > 0. Also, if Ln denotes the length of the longest induced path in Gn,p, then we find a number h(c) such that Ln is almost surely larger than (h(c) - ε)n for any ε > 0. © 1992.

Cite

CITATION STYLE

APA

Suen, W. C. S. (1992). On large induced trees and long induced paths in sparse random graphs. Journal of Combinatorial Theory, Series B, 56(2), 250–262. https://doi.org/10.1016/0095-8956(92)90021-O

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free