Small dense on-line arbitrarily partitionable graphs

Monika Bednarz, Agnieszka Burkot, Jakub Kwaśny, Kamil Pawłowski and Angelika Ryngier

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: A graph G=(V,E) is arbitrarily partitionable if for any sequence (n1,…,nk) that satisfies n1+…+nk=|G| it is possible to divide V into disjoint subsets V=V1∪…∪Vk such that |Vi|=ni,i=1,…,k and the subgraphs induced by all Vi are connected. In this paper we inspect an on-line version of this concept and show that for graphs of order n, 8≤n≤14, and size greater than (n−32)+6 these two concepts are equivalent. Although our result concerns only finitely many graphs, together with a recent theorem of Kalinowski [5] it implies that arbitrarily partitionable graphs of any order n and size greater than (n−32)+6 are also on-line arbitrarily partitionable. For the proof of our main result, we show some lemmas providing sufficient conditions for a graph to be traceable or Hamiltonian-connected, and they are of interest on their own.

Keywords: Partitions of graphs; Traceable graphs; Perfect matching (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324000547
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:470:y:2024:i:c:s0096300324000547

DOI: 10.1016/j.amc.2024.128582

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 ().