Limiting shape of the depth first search tree in an Erdos-Renyi graph

被引：7

作者：

Enriquez, Nathanael ^{[1
]}

Faraud, Gabriel ^{[1
]}

Menard, Laurent ^{[1
]}

机构：

[1] Univ Paris Nanterre, UPL, Modal X, F-92000 Nanterre, France

来源：

RANDOM STRUCTURES & ALGORITHMS | 2020年 / 56卷 / 02期

关键词：

depth first search algorithm; Erdos-Renyi graphs;

D O I：

10.1002/rsa.20878

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We show that the profile of the tree constructed by the depth first search algorithm in the giant component of an Erdos-Renyi graph with N vertices and connection probability c/N with c > 1 converges to an explicit deterministic shape. This makes it possible to exhibit a long nonintersecting path of length rho c-Li2(rho c)cxN, where rho(c) is the density of the giant component and Li-2 denotes the dilogarithm function.

引用

页码：501 / 516

页数：16

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