Factorisation of the complete graph into spanning regular factors

被引：1

作者：

Hasheminezhad, Mahdieh ^{[1
]}

McKay, Brendan D. ^{[2
]}

机构：

[1] Yazd Univ, Dept Comp Sci, Yazd, Iran

[2] Australian Natl Univ, Sch Comp, Canberra, ACT 2601, Australia

来源：

ADVANCES IN APPLIED MATHEMATICS | 2023年 / 146卷

基金：

澳大利亚研究理事会;

关键词：

ASYMPTOTIC ENUMERATION; DEGREE SEQUENCE;

D O I：

10.1016/j.aam.2023.102487

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the number of regular graphs in a simple way. This leads us to conjecture a general formula when the number of factors is vanishing compared to the number of vertices. The intermediate results include the probability that a set of moderately sparse regular graphs are edge-disjoint when randomly relabelled.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：11

共 11 条

[1]

Dinitz J. H., 1994, J COMB DES, V2, P273

[2] Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums [J].