We define new graph parameters, called flip-width, that generalize treewidth, degeneracy,
and generalized coloring numbers for sparse graphs, and clique-width and twin-width for …

The notion of bounded expansion captures uniform sparsity of graph classes and renders
various algorithmic problems that are hard in general tractable. In particular, the model …

We study two notions of being well-structured for classes of graphs that are inspired by
classic model theory. A class of graphs is monadically stable if it is impossible to define …

Monadically stable and monadically NIP classes of structures were initially studied in the
context of model theory and defined in logical terms. They have recently attracted attention …

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 …

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic
tractability: if the clique-width of a graph class ${\cal G} $ is bounded by a constant, a wide …

Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded
linear rankwidth are MSO-transductions of paths–a result that shows a strong link between …

Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded
linear rankwidth are MSO-transductions of paths. These results show a strong link between …

Low treedepth decompositions are central to the structural characterizations of bounded
expansion classes and nowhere dense classes, and the core of main algorithmic properties …

We prove that if $ G $ is a sparse graph---it belongs to a fixed class of bounded expansion
$\mathcal {C} $---and $ d\in\mathbb {N} $ is fixed, then the $ d $ th power of $ G $ can be …