Abstract
Abstract We found d 1 = d 1 ( n , p ) and d 2 = d 2 ( n , p ) such that almost every (random) graph G ∈ G ( n , p ) has retractions to d -dimensional octahedra O d for every integer d satisfying d 1 d d 2 . This result has several important consequences: (the clique complex of) the random graph has several non trivial homology/homotopy groups, the random graph is not contractible, the random graph is not homotopy equivalent to its clique graph and the random graph is clique divergent.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
