Trees with a unique maximum independent set and their linear properties

• Daniel A. Jaume ^[1] ; Gonzalo Molina ^[1] ; Rodrigo Sota ^[1]
  1. [1] Universidad Nacional de San Luis

     Universidad Nacional de San Luis

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 63, Nº. 1, 2022, págs. 223-238
• Idioma: inglés
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• Resumen

  • Trees with a unique maximum independent set encode the maximum matching structure in every tree. In this work we study some of their linear properties and give two graph operations, stellare and S-coalescence, which allow building all trees with a unique maximum independent set. The null space structure of any tree can be understood in terms of these graph operations.