Distinct sizes of maximal independent sets on graphs with restricted girth

DOI10.1051/RO/2024110MaRDI QIDQ6594025

Márcia R. Cappelle, Vinícius Gandra Martins Santos, Julliano Rosa Nascimento

Publication date: 27 August 2024

Published in: RAIRO. Operations Research (Search for Journal in Brave)

zbMATH Keywords

girthmaximal independent setswell-covered graphsindependent dominating sets

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75) Graph algorithms (graph-theoretic aspects) (05C85) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Cites Work

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• On graphs with maximal independent sets of few sizes, minimum degree at least 2, and girth at least 7
• Extending Berge's and Favaron's results about well-covered graphs
• A characterization of well covered graphs of girth 5 or greater
• A characterization of graphs of girth eight or more with exactly two sizes of maximal independent sets
• On graphs having maximal independent sets of exactly \(t\) distinct cardinalities
• A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra
• WELL-COVERED GRAPHS: A SURVEY
• On Almost Well-Covered Graphs of Girth at Least 6
• Recognizing Greedy Structures
• A classification of 1-well-covered graphs
• Some covering concepts in graphs

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