Symmetric 1-factorizations of the complete graph

被引：10
|
作者：
Pasotti, Anita [1 ]
Pellegrini, Marco Antonio [2 ]
机构：
[1] Univ Brescia, Fac Ingn, Dipartimento Matemat, I-25133 Brescia, Italy
[2] Univ Milano Bicocca, Dipartimento Matemat Pura & Applicata, I-20125 Milan, Italy
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2010年 / 31卷 / 05期
关键词：
ONE-FACTORIZATIONS; STARTERS;
D O I：
10.1016/j.ejc.2009.12.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let S(2n) be the symmetric group of degree 2n. We give a strong indication to prove the existence of a 1-factorization of the complete graph on (2n)! vertices admitting S(2n) as an automorphism group acting sharply transitively on the vertices. In particular we solve the problem when the symmetric group acts on 2p elements, for any prime p. This provides the first class of G-regular 1-factorizations of the complete graph where G is a non-soluble group. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1410 / 1418
页数：9
相关论文
共 50 条
  • [21] ON 4-SEMIREGULAR 1-FACTORIZATIONS OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
    KOBAYASHI, M
    NAKAMURA, G
    GRAPHS AND COMBINATORICS, 1994, 10 (01) : 53 - 59
  • [22] 1-factorizations of Cayley graphs
    Abdollahi, A.
    ARS COMBINATORIA, 2008, 86 : 129 - 131
  • [23] 1-Factorizations of pseudorandom graphs
    Ferber, Asaf
    Jain, Vishesh
    RANDOM STRUCTURES & ALGORITHMS, 2020, 57 (02) : 259 - 278
  • [24] Excessive near 1-factorizations
    Cariolaro, David
    Fu, Hung-Lin
    DISCRETE MATHEMATICS, 2009, 309 (14) : 4690 - 4696
  • [25] Spanning Tree Decompositions of Complete Graphs Orthogonal to Rotational 1-Factorizations
    John Caughman
    John Krussel
    James Mahoney
    Graphs and Combinatorics, 2017, 33 : 321 - 333
  • [26] 1-factorizations of pseudorandom graphs
    Ferber, Asaf
    Jain, Vishesh
    2018 IEEE 59TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), 2018, : 698 - 708
  • [27] Spanning Tree Decompositions of Complete Graphs Orthogonal to Rotational 1-Factorizations
    Caughman, John
    Krussel, John
    Mahoney, James
    GRAPHS AND COMBINATORICS, 2017, 33 (02) : 321 - 333
  • [28] Automorphism groups of graphs with 1-factorizations
    Technische Universität Dresden, Fachrichtung Mathematik, Mommsenstraße 13, 01062 Dresden, Germany
    Discrete Math, 1-3 (1-10):
  • [29] Abelian 1-factorizations in infinite graphs
    Bonvicini, S.
    Mazzuoccolo, G.
    EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (07) : 1847 - 1852
  • [30] 1-factorizations of random regular graphs
    Molloy, MSO
    Robalewska, H
    Robinson, RW
    Wormald, NC
    RANDOM STRUCTURES & ALGORITHMS, 1997, 10 (03) : 305 - 321
12345