When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

Abstract The Matching‐Cut problem is the problem to decide whether a graph has an edge
cut that is also a matching. Previously this problem was studied under the name of the …

Abstract The Independent Cutset problem asks whether there is a set of vertices in a given
graph that is both independent and a cutset. This problem is Image 1-complete even when …

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of
deciding whether or not a given graph has a matching cut, which is known to be NP …

For a connected graph G=(V, E), a subset U⊆ V is called a disconnected cut if U
disconnects the graph and the subgraph induced by U is disconnected as well. We show …

We propose the conjecture that every graph $ G $ of order $ n $ with less than $3 n-6$
edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex …

An undirected graph G=(V, E) is a bisplit graph if its vertex set can be partitioned into a
stable set and a complete bipartite graph. We provide an O (| V|| E|) time recognition …

We answer a question of Brandstädt et al. by showing that deciding whether a line graph
with maximum degree 5 has a stable cutset is NP-complete. Conversely, the existence of a …

A stable cutset in a graph G is a set S⊆ V (G) such that vertices of S are pairwise non-
adjacent and such that GS is disconnected, ie, it is both stable (or independent) set and a …

In an undirected graph, a matching cut is a partition of vertices into two sets such that the
edges across the sets induce a matching. The matching cut problem is the problem of …