Saturation numbers for disjoint stars

Zequn Lv (), Zhen He () and Mei Lu ()
Additional contact information
Zequn Lv: Tsinghua University
Zhen He: Tsinghua University
Mei Lu: Tsinghua University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 19, 17 pages

Abstract: Abstract A graph G is called an H-saturated if G does not contain H as a subgraph, but the addition of any edge between two nonadjacent vertices in G results in a copy of H in G. The saturation number sat(n, H) is the minimum number of edges in G for all H-saturated graphs G of order n. For a graph F, let mF denote the disjoint union of m copies of F. In Faudree et al. (Electron J Combin 18:19-36, 2011) Faudree, Faudree and Schmitt proposed a problem that is to determine $$sat(n,mK_{1,k})$$ s a t ( n , m K 1 , k ) for all m and k. Let $$m\ge 2$$ m ≥ 2 , $$k\ge 4$$ k ≥ 4 and $$n\ge 3mk^2$$ n ≥ 3 m k 2 . In this paper, based on linear programming models, we show that $$\begin{aligned} \left\lceil \frac{n(k-1)-\lfloor \frac{k^2}{4}\rfloor }{2} \right\rceil +m-1 \le sat(n,mK_{1,k})\le \left\lceil \frac{n(k-1)-\lfloor \frac{k^2}{4}\rfloor +3m-1}{2} \right\rceil . \end{aligned}$$ n ( k - 1 ) - ⌊ k 2 4 ⌋ 2 + m - 1 ≤ s a t ( n , m K 1 , k ) ≤ n ( k - 1 ) - ⌊ k 2 4 ⌋ + 3 m - 1 2 .

Keywords: Saturation; Stars; Flow; Digraph (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-022-00945-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00945-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-022-00945-z

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().