@inbook{c352f114656f468db92a37471c089424,
title = "Semi-random Process Without Replacement",
abstract = "We introduce and study a semi-random multigraph process, which forms a no-replacement variant of the process that was introduced in [3]. The process starts with an empty graph on the vertex set [n]. For every positive integers q and 1 ≤ r≤ n, in the ((q- 1 ) n+ r) th round of the process, the decision-maker, called Builder, is offered the vertex πq(r), where π1, π2, … is a sequence of permutations in Sn, chosen independently and uniformly at random. Builder then chooses an additional vertex (according to a strategy of his choice) and connects it by an edge to πq(r). For several natural graph properties, such as k-connectivity, minimum degree at least k, and building a given spanning graph (labeled or unlabeled), we determine the typical number of rounds Builder needs in order to construct a graph having the desired property. Along the way we introduce and analyze two urn models which may also have independent interest.",
keywords = "Games on graphs, Random process",
author = "Shoni Gilboa and Dan Hefetz",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.; European Conference on Combinatorics, Graph Theory and Applications 2021 ; Conference date: 06-09-2021 Through 10-09-2021",
year = "2021",
doi = "https://doi.org/10.1007/978-3-030-83823-2_21",
language = "الإنجليزيّة",
isbn = "9783030838225",
series = "Trends in Mathematics",
publisher = "Springer Nature",
pages = "129--135",
editor = "Jaroslav Ne{\v s}et{\v r}il",
booktitle = "Extended Abstracts EuroComb 2021",
address = "الولايات المتّحدة",
}