Packing 2- and 3-stars into cubic graphs

Wenying Xi, Wensong Lin and Yuquan Lin

Applied Mathematics and Computation, 2024, vol. 460, issue C

Abstract: Let i be a positive integer. A complete bipartite graph K1,i is called an i-star, denoted by Si. An {S2,S3}-packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum {S2,S3}-packing problem is to find an {S2,S3}-packing of a given graph containing the maximum number of vertices. The perfect {S2,S3}-packing problem is to answer whether there is an {S2,S3}-packing containing all vertices of the given graph. The perfect {S2,S3}-packing problem is NP-complete in general graphs. In this paper, we prove that the perfect {S2,S3}-packing problem remains NP-complete in cubic graphs and that every simple cubic graph has an {S2,S3}-packing covering at least six-sevenths of its vertices. Our proof infers a quadratic-time algorithm for finding such an {S2,S3}-packing of a simple cubic graph.

Keywords: Star family; Packing; Cubic graph; Quadratic-time algorithm (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323004563
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:460:y:2024:i:c:s0096300323004563

DOI: 10.1016/j.amc.2023.128287

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 ().