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

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

Abstract

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 .