Even-cycle systems with prescribed automorphism groups

被引：6

作者：

Grannell, M. J. ^{[1
]}

Griggs, T. S. ^{[1
]}

Lovegrove, G. J. ^{[1
]}

机构：

[1] Open Univ, Dept Math & Stat, Milton Keynes MK7 6AA, Bucks, England

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2013年 / 21卷 / 04期

关键词：

automorphism group; cycle system; DECOMPOSITIONS; EXISTENCE; GRAPHS;

D O I：

10.1002/jcd.21334

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that for any finite group Gamma, there exists a 2k-cycle system whose full automorphism group is isomorphic to Gamma. Furthermore, the minimal order of such a system is at most 8k gamma log(2) gamma+1, where gamma = vertical bar Gamma vertical bar. (C) 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 142-156, 2013

引用

页码：142 / 156

页数：15

共 13 条

[1] Cycle decompositions of Kn and Kn-I
Alspach, B
Gavlas, H
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2001, 81 (01) : 77 - 99
[2] BABAI L, 1993, J LOND MATH SOC, V47, P417
[3] Babai L., 1974, CAN MATH B, V17, p467 470
[4] Rotational k-cycle systems of order ν < 3k;: Another proof of the existence of odd cycle systems
Buratti, M
[J]. JOURNAL OF COMBINATORIAL DESIGNS, 2003, 11 (06) : 433 - 441
[5] Existence of cyclic k-cycle systems of the complete graph
Buratti, M
Del Fra, A
[J]. DISCRETE MATHEMATICS, 2003, 261 (1-3) : 113 - 125
[6] Dejter I. J., 1987, J COMBIN MATH COMBIN, V16, p129 152
[7] GRAPHS OF DEGREE 3 WITH A GIVEN ABSTRACT GROUP
FRUCHT, R
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1949, 1 (04): : 365 - 378
[8] Frucht R., 1938, Compositio Mathematica, V6, P239
[9] ON THE CONSTRUCTION OF ODD CYCLE SYSTEMS
HOFFMAN, DG
LINDNER, CC
RODGER, CA
[J]. JOURNAL OF GRAPH THEORY, 1989, 13 (04) : 417 - 426
[10] Lovegrove G.J., 2008, THESIS OPEN U

← 1 2 →