Structural properties and characterizations of ${\mathbf{W}}_p$ class

Abstract

We establish new characterizations of graphs belonging to the ${\mathbf{W}}_p$ class. In addition, we characterize locally triangle-free $\hat{I}\pm$-critical graphs in this class. As a consequence, our results yield a partial answer to a question raised by Plummer \cite{Plum93} in the case $p=2$.

13 pages