A new width parameter of graphs based on edge cuts: α-edge-crossing width

We introduce graph width parameters, called α-edge-crossing width and edge-crossing width. These are defined in terms of the number of edges crossing a bag of a tree-cut decomposition. They are motivated by edge-cut width, recently introduced by Brand et al. (2022). We show that edge-crossing width...

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Veröffentlicht in:Discrete Applied Mathematics Jg. 380; S. 492 - 510
Hauptverfasser: Chang, Yeonsu, Kwon, O-joung, Lee, Myounghwan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.02.2026
Schlagworte:
[formula omitted]-edge-crossing width
FPT algorithm
List coloring
α-edge-crossing width
List coloring
FPT algorithm
ISSN:0166-218X
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Zusammenfassung:We introduce graph width parameters, called α-edge-crossing width and edge-crossing width. These are defined in terms of the number of edges crossing a bag of a tree-cut decomposition. They are motivated by edge-cut width, recently introduced by Brand et al. (2022). We show that edge-crossing width is equivalent to the known parameter tree-partition-width. On the other hand, α-edge-crossing width is a new parameter; tree-cut width and α-edge-crossing width are incomparable, and they both lie between tree-partition-width and edge-cut width. We provide an algorithm that, for a given n-vertex graph G and integers k and α, in time 2O((α+k)log(α+k))n2 either outputs a tree-cut decomposition certifying that the α-edge-crossing width of G is at most 2α2+5k or confirms that the α-edge-crossing width of G is more than k. As applications, for every fixed α, we obtain FPT algorithms for the List Coloring and Precoloring Extension problems parameterized by α-edge-crossing width. They were known to be W[1]-hard parameterized by tree-partition-width, and FPT parameterized by edge-cut width, and we close the complexity gap between these two parameters.
ISSN:0166-218X
DOI:10.1016/j.dam.2025.10.056