Abstract
AbstractLet G be a d‐regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ which is second largest in absolute value satisfies λ = o(d). Let Gp with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of Gp is O(log n) and if α > 1, then Gp contains a unique giant component of size Ω(n), with all other components of size O(log n). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.