Graphic sequences with a realization containing cycles C3,…,Cℓ

Jian-Hua Yin, Kun Ye and Jia-Yun Li

Applied Mathematics and Computation, 2019, vol. 353, issue C, 88-94

Abstract: A non-increasing sequence π=(d1,…,dn) of nonnegative integers is said to be graphic if it is realizable by a simple graph G on n vertices. A graphic sequence π=(d1,…,dn) is said to be potentially3Cℓ-graphic if there is a realization of π containing cycles of every length r, 3 ≤ r ≤ ℓ. Li et al. proposed a problem about giving a criteria of potentially 3Cℓ-graphic sequences. For ℓ=5,6, Chen et al. investigated this problem and showed that if dℓ≥ℓ2, then π is potentially 3Cℓ-graphic. In this paper, we extend the above results of Chen et al. for ℓ=5,6 to the general case ℓ ≥ 5, and prove that for every integer ℓ ≥ 5, if dℓ≥ℓ2, then π is potentially 3Cℓ-graphic.

Keywords: Graphic sequence; Realization; Potentially 3Cℓ-graphic sequence (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319301018
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:353:y:2019:i:c:p:88-94

DOI: 10.1016/j.amc.2019.02.003

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().