A note on rainbow saturation number of paths

Shujuan Cao, Yuede Ma and Zhenyu Taoqiu

Applied Mathematics and Computation, 2020, vol. 378, issue C

Abstract: For a fixed graph F and an integer t, the rainbow saturation number of F, denoted by satt(n,R(F)), is defined as the minimum number of edges in a t-edge-colored graph on n vertices which does not contain a rainbow copy of F, i.e., a copy of F all of whose edges receive a different color, but the addition of any missing edge in any color from [t] creates such a rainbow copy. Barrus, Ferrara, Vardenbussche and Wenger prove that satt(n,R(Pℓ))≥n−1 for ℓ ≥ 4 and satt(n,R(Pℓ))≤⌈nℓ−1⌉·(ℓ−12) for t≥(ℓ−12), where Pℓ is a path with ℓ edges. In this short note, we improve the upper bounds and show that satt(n,R(Pℓ))≤⌈nℓ⌉·((ℓ−22)+4) for ℓ ≥ 5 and t≥2ℓ−5.

Keywords: Rainbow saturation number; Edge-coloring; Path (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320301739
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:378:y:2020:i:c:s0096300320301739

DOI: 10.1016/j.amc.2020.125204

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 ().