A note on the independence number, domination number and related parameters of random binary search trees and random recursive trees

被引：4

作者：

Fuchs, Michael ^{[1
]}

Holmgren, Cecilia ^{[2
]}

Mitsche, Dieter ^{[3
]}

Neininger, Ralph ^{[4
]}

机构：

[1] Natl Chengchi Univ, Dept Math Sci, Taipei, Taiwan

[2] Uppsala Univ, Dept Math, Uppsala, Sweden

[3] Univ Lyon, Univ Jean Monnet, Inst Camille Jordan UMR 5208, Lyon, France

[4] Goethe Univ Frankfurt, Inst Math, Frankfurt, Germany

来源：

DISCRETE APPLIED MATHEMATICS | 2021年 / 292卷

关键词：

Independence number; Domination number; Clique cover number; Random recursive trees; Random binary search trees; Fringe trees; Central limit laws; LIMIT LAWS; ALGORITHMS; SETS;

D O I：

10.1016/j.dam.2020.12.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We identify the mean growth of the independence number of random binary search trees and random recursive trees and show normal fluctuations around their means. Similarly we also show normal limit laws for the domination number and variations of it for these two cases of random tree models. Our results are an application of a recent general theorem of Holmgren and Janson on fringe trees in these two random tree models. (C) 2020 Published by Elsevier B.V.

引用

页码：64 / 71

页数：8

共 50 条

[21] A NOTE ON THE p- DOMINATION NUMBER OF TREES
Lu, You
Hou, Xinmin
Xu, Jun-Ming
OPUSCULA MATHEMATICA, 2009, 29 (02) : 157 - 164
[22] Phase changes in subtree varieties in random recursive and binary search trees
Feng, Qunqiang
Mahmoud, Hosam M.
Panholzer, Alois
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2008, 22 (01) : 160 - 184
[23] WEAK CONVERGENCE OF THE NUMBER OF VERTICES AT INTERMEDIATE LEVELS OF RANDOM RECURSIVE TREES
Iksanov, Alexander
Kabluchko, Zakhar
JOURNAL OF APPLIED PROBABILITY, 2018, 55 (04) : 1131 - 1142
[24] Martingales on Trees and the Empire Chromatic Number of Random Trees
Cooper, Colin
McGrae, Andrew R. A.
Zito, Michele
FUNDAMENTALS OF COMPUTATION THEORY, PROCEEDINGS, 2009, 5699 : 74 - +
[25] Note on the outdegree of a node in random recursive trees
Mehri Javanian
Mohammad Q. Vahidi-Asl
Journal of Applied Mathematics and Computing, 2003, 13 (1-2) : 99 - 103
[26] Patterns in random binary search trees
Flajolet, P
Gourdon, X
Martinez, C
RANDOM STRUCTURES & ALGORITHMS, 1997, 11 (03) : 223 - 244
[27] A note on random suffix search trees
Devroye, L
Neininger, R
MATHEMATICS AND COMPUTER SCIENCE II: ALGORITHMS, TREES, COMBINATORICS AND PROBABILITIES, 2002, : 267 - 278
[28] The Distribution of the Number of Automorphisms of Random Trees
Olsson C.
Wagner S.
La Matematica, 2023, 2 (3): : 743 - 771
[29] Binarization Trees and Random Number Generation
Pae, Sung-Il
IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (04) : 2581 - 2587
[30] Random Recursive Trees and Preferential Attachment Trees are Random Split Trees
Janson, Svante
COMBINATORICS PROBABILITY & COMPUTING, 2019, 28 (01): : 81 - 99

← 1 2 3 4 5 →