论文标题
适当的k混合薄图的双宽度和转导
Twin-width and Transductions of Proper k-Mixed-Thin Graphs
论文作者
论文摘要
由Bonnet，Kim，Thomass E和Watrigant在2020年推出的新图形参数双宽度允许使用FPT算法来测试图形的所有FO属性。从算法的角度来看，这使得有效界限的双宽度有吸引力。特别是，有效界限的双宽度的类别包括适当的间隔图，以及（作为Digraphs）宽度k的posets。受到间隔图的现有概括为所谓的k-thin图的启发，我们定义了一类新的合适的k混合图形图，该图在很大程度上概括了适当的间隔图。我们证明，合适的k混合图在k中具有双宽线性，并且k混合薄的图的轻微子类与宽度k'的poset相等，因此k和k之间存在二次聚集关系。除此之外，我们还提供了所谓的红色潜在方法的抽象概述，我们用来证明我们的双宽度界限。
The new graph parameter twin-width, introduced by Bonnet, Kim, Thomass e and Watrigant in 2020, allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the algorithmic point of view. In particular, classes of efficiently bounded twin-width include proper interval graphs, and (as digraphs) posets of width k. Inspired by an existing generalization of interval graphs into so-called k-thin graphs, we define a new class of proper k-mixed-thin graphs which largely generalizes proper interval graphs. We prove that proper k-mixed-thin graphs have twin-width linear in k, and that a slight subclass of k-mixed-thin graphs is transduction-equivalent to posets of width k' such that there is a quadratic-polynomial relation between k and k'. In addition to that, we also give an abstract overview of the so-called red potential method which we use to prove our twin-width bounds.
