Graph-indexed random walks on pseudotrees

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.045

Jan Bok , Jaroslav Nešetřil

引用次数: 2

Abstract

We investigate the average range of 1-Lipschitz mappings (graph-indexed random walks) of a given connected graph. This parameter originated in statistical physics, it is connected to the study of random graph homomorphisms and generalizes standard random walks on $Z$ .

Our first goal is to prove a closed-form formula for this parameter for cycle graphs. The second one is to prove two conjectures, the first by Benjamini, Häggström and Mossel and the second by Loebl, Nešetřil and Reed, for unicyclic graphs. This extends a result of Wu, Xu, and Zhu [5] who proved the aforementioned conjectures for trees.

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伪树上的图索引随机漫步

我们研究了给定连通图的1-Lipschitz映射(图索引随机游走)的平均范围。这个参数起源于统计物理，它与随机图同态的研究有关，并推广了z上的标准随机行走。我们的第一个目标是证明循环图上这个参数的一个封闭形式公式。第二个是证明关于单环图的两个猜想，第一个是Benjamini, Häggström和Mossel的猜想，第二个是Loebl, Nešetřil和Reed的猜想。这扩展了Wu、Xu和Zhu[5]的结果，他们证明了上述关于树木的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

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