On the existence of unparalleled even cycle systems

被引：1

作者：

Danziger, Peter ^{[1
]}

Mendelsohn, Eric ^{[1
]}

Traetta, Tommaso ^{[1
]}

机构：

[1] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2017年 / 59卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

STEINER TRIPLE-SYSTEMS; OBERWOLFACH-PROBLEM; COMPLETE GRAPH; LATIN SQUARES; FACTORIZATIONS; DECOMPOSITIONS;

D O I：

10.1016/j.ejc.2016.07.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A 2t-cycle system of even order v is a set C of cycles of length 2t whose edges partition the edge-set of K-v - I (i.e., the complete graph minus the 1-factor I). If v equivalent to 0 (mod 2t), a set of v/2t vertex disjoint cycles of C is a parallel class. If C has no parallel classes, we call such a system unparalleled. We show that there exists an unparalleled 2t-cycle system of order v equivalent to 0 (mod 2t) if and only if v > 2t > 2. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：11 / 22

页数：12

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