# Giant Components in Random Temporal Graphs

@article{Becker2022GiantCI, title={Giant Components in Random Temporal Graphs}, author={Ruben Becker and Arnaud Casteigts and Pierluigi Crescenzi and Bojana Kodric and Malte Renken and Michael A. Raskin and Viktor Zamaraev}, journal={ArXiv}, year={2022}, volume={abs/2205.14888} }

A temporal graph is a graph whose edges appear only at certain points in time. In these graphs, reachability among the nodes relies on paths that traverse edges in chronological order ( temporal paths ). Unlike standard paths, temporal paths are not always composable, thus the reachability relation is not transitive and connected components do not form equivalence classes. We investigate the evolution of connected components in a simple model of random temporal graphs. In this model, a random…

## References

SHOWING 1-10 OF 17 REFERENCES

### Sharp Thresholds in Random Simple Temporal Graphs

- Mathematics, Computer Science2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

This paper considers a simple model of random temporal graph obtained from an Erdös-Rényi random graph G ~ Gn,p by considering a random permutation of the edges and interpreting the ranks in π as presence times and shows that temporal reachability in this model exhibits a surprisingly regular sequence of thresholds.

### Complexity of Connected Components in Evolving Graphs and the Computation of Multicast Trees in Dynamic Networks

- Computer ScienceADHOC-NOW
- 2003

This paper first shows that computing different types of strongly connected components in evolving digraphs is NP-Complete, and then proposes an algorithm to build all rooted directed minimum spanning trees in strongly connected dynamic networks.

### Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis. 2nd

- 2017

### Finding Temporal Paths Under Waiting Time Constraints

- Computer ScienceAlgorithmica
- 2021

This work investigates a basic constraint for temporal paths, and explores several natural parameterizations, presenting FPT algorithms for three kinds of parameters: output-related parameters (here, the maximum length of the path), classical parameters applied to the underlying graph (e.g., feedback edge number), and a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph.

### Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs

- Mathematics, Computer ScienceMFCS
- 2020

An algorithm for enumerating all the minimal s-d separators in a DAG with O(nm) delay, where n and m are respectively the number of nodes and arcs, and the delay is the time between the output of two consecutive solutions.

### Assigning times to minimise reachability in temporal graphs

- MathematicsJ. Comput. Syst. Sci.
- 2021

### Introduction to Random Graphs

- Computer Science
- 2016

All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

### WEIGHTED SUMS OF CERTAIN DEPENDENT RANDOM VARIABLES

- Mathematics
- 1967

1. Let be a probability space and,be an increasing family of sub o'-fields of(we put(c) Let (xn)n=1, 2, •c be a sequence of bounded martingale differences on , that is,xn(ƒÖ) is bounded almost surely…

### Deleting edges to restrict the size of an epidemic in temporal networks

- Computer ScienceJ. Comput. Syst. Sci.
- 2021

### Temporal Graph Classes: A View Through Temporal Separators

- MathematicsWG
- 2018

This work investigates the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph and identifies sharp borders between tractable and intractable cases.