The rank-width is a graph parameter related in terms of fixed functions to clique-width but
more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is …

We prove that one can express the vertex-minor relation on finite undirected graphs by
formulas of monadic second-order logic (with no edge set quantification) extended with a …

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 …

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Vertex-deletion problems have been at the heart of parameterized complexity throughout its
history. Here, the aim is to determine the minimum size (denoted by mod ℋ) of a modulator …

Vertex deletion problems have been at the heart of numerous major advances in Algorithms
and Combinatorial Optimization, and especially so in the area of Parameterized Complexity …

AC-coloured graph is a graph, that is possibly directed, where the edges are coloured with
colours from the set C. Clique-width is a complexity measure for C-coloured graphs, for finite …

We define rank-width of graphs to investigate clique-width. Rank-width is a complexity
measure of decomposing a graph in a kind of tree-structure, called a rank-decomposition …

We prove a precise min-max theorem for the following problem. Let $ G $ be an Eulerian
graph with a specified set of edges $ S\subseteq E (G) $, and let $ b $ be a vertex of $ G …

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 …