perfect graphs
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Structure of super strongly perfect graphs

2021 ◽  
Author(s):  
T. E. Soorya ◽  
Sunil Mathew
Keyword(s):  
Line Graph ◽  
Perfect Graphs ◽  
Split Graph ◽  
Counter Example ◽  
Existing Result

Super strongly perfect graphs and their association with certain other classes of graphs are discussed in this paper. It is observed that every split graph is super strongly perfect. An existing result on super strongly perfect graphs is disproved providing a counter example. It is also established that if a graph [Formula: see text] contains a cycle of odd length, then its line graph [Formula: see text] is not always super strongly perfect. Complements of cycles of length six or above are proved to be non-super strongly perfect. If a graph is strongly perfect, then it is shown that they are super strongly perfect and hence all [Formula: see text]-free graphs are super strongly perfect.

scholarly journals Nearly Gorenstein Rings Arising from Finite Graphs

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Takayuki Hibi ◽  
Dumitru I. Stamate
Keyword(s):  
Perfect Graphs ◽  
Stable Set ◽  
Gorenstein Rings ◽  
Finite Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.

Two classes of β-perfect graphs that do not necessarily have simplicial extremes

2021 ◽  
Vol 344 (7) ◽  
pp. 112374
Author(s):  
Jake Horsfield ◽  
Kristina Vušković
Keyword(s):  
Perfect Graphs

A Note on St-Coloring of Some Non Perfect Graphs

2021 ◽  
pp. 112-119
Author(s):  
Rubul Moran ◽  
Aditya Pegu ◽  
I. J. Gogoi ◽  
A. Bharali
Keyword(s):  
Perfect Graphs

scholarly journals New examples of minimal non-strongly-perfect graphs

2021 ◽  
Vol 344 (5) ◽  
pp. 112334
Author(s):  
Maria Chudnovsky ◽  
Cemil Dibek ◽  
Paul Seymour
Keyword(s):  
Perfect Graphs

scholarly journals Some classes of Trivially Perfect Graphs

2021 ◽  
Vol 1770 (1) ◽  
pp. 012074
Author(s):  
G. R. Gandal ◽  
R. Mary Jeya Jothi
Keyword(s):  
Perfect Graphs

Super strongly perfect graphs

2021 ◽  
pp. 2150088
Author(s):  
Vrinda Mary Mathew ◽  
Joseph Varghese Kureethara
Keyword(s):  
Perfect Graphs

Some of the published results on super strongly perfect graphs are found to be erroneous. We provide some examples and counter examples on the concepts associated with super strongly perfects.

scholarly journals Perfect Graphs for Domination Games

2021 ◽  
Author(s):  
Csilla Bujtás ◽  
Vesna Iršič ◽  
Sandi Klavžar
Keyword(s):  
Perfect Graphs
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