D $ D $ -有限预算随机图的连通性

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-09-18 DOI:10.1002/jgt.23180

Lyuben Lichev

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引用次数: 0

摘要

在这篇短文中，我们考虑Frieze、Krivelevich和Michaeli最近引入的一个图形过程。在他们的模型中，完整图K n ${K}_{n}$的边是随机排列的，然后连续地显示给一个叫做Builder的玩家。在每一轮，建设者必须决定他们是否接受在这一轮提出的优势。我们证明，对于每一个d≥2 $d\ge 2$，Builder可以在(1 + 0(1)之后构造一个生成d $d$连通图)) n log n / 2 $(1+o(1))n\mathrm{log}\unicode{x0200A}n/2$通过接受1 + 0 (1)) d n / 2$(1+o(1))dn/2$当n→∞时概率收敛到1的边$n\to \infty $。这就解决了弗里兹、克里维列维奇和米切利的一个猜想。

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d $d$ -connectivity of the random graph with restricted budget

In this short note, we consider a graph process recently introduced by Frieze, Krivelevich and Michaeli. In their model, the edges of the complete graph $K_{n}$ are ordered uniformly at random and are then revealed consecutively to a player called Builder. At every round, Builder must decide if they accept the edge proposed at this round or not. We prove that, for every $d \geq 2$ , Builder can construct a spanning $d$ -connected graph after $(1 + o (1)) n \log n / 2$ rounds by accepting $(1 + o (1)) d n / 2$ edges with probability converging to 1 as $n \to \infty$ . This settles a conjecture of Frieze, Krivelevich and Michaeli.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .