1-well-covered graphs containing a clique of size n/3
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Inst Teknologi Bandung
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
A graph is well-covered if all of its maximal independent sets have the same size. A graph that remains well-covered upon the removal of any vertex is called a 1-well-covered graph. These graphs, when they have no isolated vertices, are also known as W-2 graphs. It is well-known that every graph G is an element of W-2 has two disjoint maximum independent sets. In this paper, we investigate connected W-2 graphs with n vertices that contain a clique of size n/3. We prove that if the removal of two disjoint maximum independent sets from a graph G is an element of W-2 leaves a clique of size at least 3, then G contains a clique of size n/3. Using this result, we provide a complete characterization of these graphs, based on eleven graph families.
Açıklama
Anahtar Kelimeler
independent set, clique, matching, well-covered
Kaynak
Electronic Journal of Graph Theoryand Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
12
Sayı
2
