Rainbow numbers for paths in planar graphs

Zhongmei Qin, Shasha Li, Yongxin Lan and Jun Yue

Applied Mathematics and Computation, 2021, vol. 397, issue C

Abstract: Given a family of graphs F and a subgraph H of F∈F, let rb(F,H) denote the smallest number k so that there is a rainbow H in any k-edge-colored F. We call it rainbow number for H in regard to F. The set of all plane triangulations of order n is denoted by Tn. The wheel graph of order d+1 and the path of order k are denoted by Wd and Pk, respectively. In this paper, we establish lower bounds of rb(Tn,Pk) for all k≥8, which improves the results in [Y. Lan, Y. Shi and Z-X. Song, Planar anti-Ramsey numbers for paths and cycles, Discrete Math. 342(11) (2019), 3216–3224.]. In addition, we also attain the accurate values or bounds of rb(Tn,Pk) for 4≤k≤7. Furthermore, we get lower and upper bounds of rb(Wd,Pk) for all k≥9 and obtain the accurate values of rb(Wd,Pk) for k∈{4,5,6,7,8,d+1}.

Keywords: Rainbow number; Plane triangulation; Path; Wheel graph (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320308717
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:397:y:2021:i:c:s0096300320308717

DOI: 10.1016/j.amc.2020.125918

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 ().