Document Type

Article

Publication Date

1-1-2023

Abstract

A graph in which every connected induced subgraph has a disconnected complement is called a cograph. Such graphs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We define a 2-cograph to be a graph in which the complement of every 2-connected induced subgraph is not 2-connected. We show that, like cographs, 2-cographs can be recursively defined and are closed under induced minors. We characterize the class of non-2-cographs for which every proper induced minor is a 2-cograph. We further find the finitely many members of this class whose complements are also induced-minor-minimal non-2-cographs.

Publication Source (Journal or Book title)

Electronic Journal of Combinatorics

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