Maximal independent sets in bipartite graphs with at least one cycle - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2013

Maximal independent sets in bipartite graphs with at least one cycle

Abstract

A maximal independent set is an independent set that is not a proper subset of any other independent set. Liu [J.Q. Liu, Maximal independent sets of bipartite graphs, J. Graph Theory, 17 (4) (1993) 495-507] determined the largest number of maximal independent sets among all n-vertex bipartite graphs. The corresponding extremal graphs are forests. It is natural and interesting for us to consider this problem on bipartite graphs with cycles. Let \mathscrBₙ (resp. \mathscrBₙ') be the set of all n-vertex bipartite graphs with at least one cycle for even (resp. odd) n. In this paper, the largest number of maximal independent sets of graphs in \mathscrBₙ (resp. \mathscrBₙ') is considered. Among \mathscrBₙ the disconnected graphs with the first-, second-, \ldots, \fracn-22-th largest number of maximal independent sets are characterized, while the connected graphs in \mathscrBₙ having the largest, the second largest number of maximal independent sets are determined. Among \mathscrBₙ' graphs have the largest number of maximal independent sets are identified.
Fichier principal
Vignette du fichier
2363-8315-2-PB.pdf (244.5 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00980771 , version 1 (18-04-2014)

Identifiers

Cite

Shuchao Li, Huihui Zhang, Xiaoyan Zhang. Maximal independent sets in bipartite graphs with at least one cycle. Discrete Mathematics and Theoretical Computer Science, 2013, Vol. 15 no. 2 (2), pp.243--258. ⟨10.46298/dmtcs.607⟩. ⟨hal-00980771⟩

Collections

TDS-MACS
237 View
1209 Download

Altmetric

Share

Gmail Facebook X LinkedIn More