Structural Lemmas on Temporal Connectivity

2026-06-14

AI Summary

This study addresses the lack of a systematic theoretical characterization of temporal connectivity structures in temporal graphs. By revisiting and reconstructing key ideas from rumor propagation theories developed between the 1970s and 1990s, and integrating original analytical insights, this work introduces a series of structural lemmas within the framework of “simple and proper” (i.e., “happy”) temporal graphs. These lemmas collectively reveal the intrinsic principles governing temporal connectivity. The paper establishes the first foundational theoretical framework specifically tailored to temporal connectivity, thereby providing a rigorous basis for the design of efficient algorithms and the analysis of dynamic complex networks.

Abstract

This paper presents several lemmas on the structure of temporal connectivity in temporal graphs. Some of these lemmas are adapted from the literature on gossip from the 70-90's and reformulated in the context of temporal graph theory. Many others are original. For ease of presentation and for avoiding lengthy case distinctions, we formulate all the lemmas in the setting of simple and proper (a.k.a, happy) temporal graphs, discussing occasionally their generality beyond this setting.

Problem

• temporal graphs
• temporal connectivity
• structural lemmas
• time-varying networks
• graph theory

Innovation

• temporal graphs
• temporal connectivity
• structural lemmas
• gossip protocols
• happy temporal graphs