Structural properties and characterizations of W_p class

2025/09/04 by Hoang, Do Trong, Levit, Vadim E., Mandrescu, Eugen
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.03847

Abstract

We establish new characterizations of graphs belonging to the W_p class. In addition, we characterize locally triangle-free α-critical graphs in this class. As a consequence, our results yield a partial answer to a question raised by Plummer \citePlum93 in the case p=2.

Citations

• Log-concavity of the independence polynomials of W_p graphs
• The Roller-Coaster Conjecture Revisited
• 1-well-covered graphs revisited
• Buchsbaumness of the second powers of edge ideals
• On well-covered, vertex decomposable and Cohen-Macaulay graphs

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