Threshold functions in random subgraph counting in the random-connection model

• Main Author: Chan, Luo Xi
• Other Authors: Nicolas Privault
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Mathematical Sciences; Random-connection model; Threshold; Subgraph containment
• Online Access: https://hdl.handle.net/10356/175628
• Institution: Nanyang Technological University

Random-connection model serves as a prominent graph model other than the Erdős-Rényi model and the random geometric graph. The majority of the properties in the random-connection model has yet to be found. This thesis follows on from previous research on the normal approximation of subgraph counts and graph connectivity to explore random subgraph containment in the random-connection model. In the dilute regime, an arbitrary graph G with at least one edge is asymptotically almost surely can be found in the corresponding model G_(H_λ ) (Ξ). While for the sparse regime, the relation between c_λ and λ^(-M(G)) serves as a possible threshold function for the subgraph containment.