Recently, hardness results for problems in P were achieved using reasonable complexity-
theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these …

The recent increase of interest in the graph invariant called tree-depth and in its applications
in algorithms and logic on graphs led to a natural question: is there an analogously useful" …

Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In
this context, vertex cover is used as a powerful parameter for dealing with graph problems …

Short Survey of Obstruction to Rank-width and Linear Rank Width Page 1 592 Int. j. adv.
multidisc. res. stud. 2024; 4(4):592-596 Short Survey of Obstruction to Rank-width and Linear …

Parameterized algorithms are a very useful tool for dealing with NP-hard problems on
graphs. In this context, vertex cover is used as a powerful parameter for dealing with …

The investigation of width parameters in both graph and algebraic contexts has garnered
significant interest. Among these parameters, the linear branch width has emerged as a …

Research in graph theory remains essential for driving progress in both scientific and
technological fields. Within this area, studies on graph algorithms and those leveraging …

In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width,
and linear rank-width for directed graphs. We compare these parameters with each other as …

We show that for every forest T the linear rank-width of T is equal to the path-width of T, and
the linear clique-width of T equals the path-width of T plus two, provided that T contains a …

Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid
path-width. In this paper, we show that the linear rank-width of every n-vertex distance …