Coverings, Matchings and the number of maximal independent sets of graphs
Do Trong Hoang, Tran Nam Trung
TL;DR
This paper establishes bounds on the maximum number of maximal independent sets in graphs based on their covering numbers and characterizes extremal graphs, also extending results to K"onig-Egerváry graphs using matching numbers.
Contribution
It provides a complete characterization of extremal graphs with maximum maximal independent sets based on covering numbers and extends the analysis to K"onig-Egerváry graphs.
Findings
Maximum number of maximal independent sets in graphs determined by covering numbers
Complete characterization of extremal graphs for this maximum
Extension of results to K"onig-Egerváry graphs using matching numbers
Abstract
We determine the maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers and we completely characterize the extremal graphs. As an application, we give a similar result for K\"onig-Egerv\'ary graphs in terms of their matching numbers.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory