BROWSE

Related Scientist

Casey, Tompkins's photo.

Casey, Tompkins
이산수학 그룹
more info

ITEM VIEW & DOWNLOAD

Long path and cycle decompositions of even hypercubes

Cited 0 time in webofscience Cited 0 time in scopus
17 Viewed 0 Downloaded
Title
Long path and cycle decompositions of even hypercubes
Author(s)
Axenovich, Maria; Offner, David; Casey Tompkins
Publication Date
2021-06
Journal
EUROPEAN JOURNAL OF COMBINATORICS, v.95
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Abstract
©2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). We consider edge decompositions of the n-dimensional hypercube Q(n) into isomorphic copies of a given graph H. While a number of results are known about decomposing Q n into graphs from various classes, the simplest cases of paths and cycles of a given length are far from being understood. A conjecture of Erde asserts that if n is even, l < 2(n) and l divides the number of edges of Q(n), then the path of length l decomposes Q(n). Tapadia et al. proved that any path of length 2(m)n, where 2(m) < n, satisfying these conditions decomposes Q. Here, we make progress toward resolving Erde's conjecture by showing that cycles of certain lengths up to 2(n+1) /n decompose Q(n) As a consequence, we show that Q n can be decomposed into copies of any path of length at most 2(n)/n dividing the number of edges of Q(n), thereby settling Erde's conjecture up to a linear factor. (C) 2021 The Author(s). Published by Elsevier Ltd.
URI
https://pr.ibs.re.kr/handle/8788114/10031
DOI
10.1016/j.ejc.2021.103320
ISSN
0195-6698
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
Files in This Item:
There are no files associated with this item.

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse