A greedy algorithm for finding a large 2-matching on a random cubic graph

被引：0

作者：

Bal, Deepak ^{[1
]}

Bennett, Patrick ^{[2
]}

Bohman, Tom ^{[3
]}

Frieze, Alan ^{[3
]}

机构：

[1] Montclair State Univ, Dept Math Sci, Montclair, NJ USA

[2] Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA

[3] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

JOURNAL OF GRAPH THEORY | 2018年 / 88卷 / 03期

基金：

美国国家科学基金会;

关键词：

greedy algorithm; 2-matching; random cubic graph; SPARSE RANDOM GRAPHS; HAMILTON CYCLES; REGULAR GRAPHS; MINIMUM DEGREE; KARP-SIPSER;

D O I：

10.1002/jgt.22224

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A 2-matching of a graph G is a spanning subgraph with maximum degree two. The size of a 2-matching U is the number of edges in U and this is at least n-(U) where n is the number of vertices of G and denotes the number of components. In this article, we analyze the performance of a greedy algorithm 2greedy for finding a large 2-matching on a random 3-regular graph. We prove that with high probability, the algorithm outputs a 2-matching U with (U) = Theta(n(1/5)).

引用

页码：449 / 481

页数：33

共 36 条

[1] On a Greedy 2-Matching Algorithm and Hamilton Cycles in Random Graphs with Minimum Degree at Least Three
Frieze, Alan
[J]. RANDOM STRUCTURES & ALGORITHMS, 2014, 45 (03) : 443 - 497
[2] THE 2-MATCHING LATTICE OF A GRAPH
JUNGNICKEL, D
LECLERC, M
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1989, 46 (02) : 246 - 248
[3] Bipartite double cover and perfect 2-matching covered graph with its algorithm
Gan, Zhiyong
Lou, Dingjun
Zhang, Zanbo
Wen, Xuelian
[J]. FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (03) : 621 - 634
[4] Bipartite double cover and perfect 2-matching covered graph with its algorithm
Zhiyong Gan
Dingjun Lou
Zanbo Zhang
Xuelian Wen
[J]. Frontiers of Mathematics in China, 2015, 10 : 621 - 634
[5] A simple algorithm for finding a maximum triangle-free 2-matching in subcubic graphs
Kobayashi, Yusuke
[J]. DISCRETE OPTIMIZATION, 2010, 7 (04) : 197 - 202
[6] Finding a maximum 2-matching excluding prescribed cycles in bipartite graphs
Takazawa, Kenjiro
[J]. DISCRETE OPTIMIZATION, 2017, 26 : 26 - 40
[7] Finding a large hidden clique in a random graph
Alon, N
Krivelevich, M
Sudakov, B
[J]. RANDOM STRUCTURES & ALGORITHMS, 1998, 13 (3-4) : 457 - 466
[8] Analysis of greedy algorithm for vertex covering of random graph by cubes
Toman, Eduard
Stanek, Martin
[J]. COMPUTING AND INFORMATICS, 2006, 25 (05) : 393 - 404
[9] MATCHING INDEX AND ITS ALGORITHM OF UNCERTAIN RANDOM GRAPH
Zhang, B.
Peng, J.
Li, S.
[J]. APPLIED AND COMPUTATIONAL MATHEMATICS, 2018, 17 (01) : 22 - 35
[10] A fast scaling algorithm for the weighted triangle-free 2-matching problem
Artamonov, S.
Babenko, M.
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2018, 68 : 3 - 23

← 1 2 3 4 →