A New Width Parameter of Graphs Based on Edge Cuts: α-Edge-Crossing Width
- Authors
- Chang, Yeonsu; Kwon, O-joung; Lee, Myounghwan
- Issue Date
- Sep-2023
- Publisher
- Springer Science and Business Media Deutschland GmbH
- Keywords
- FPT algorithm; List Coloring; α-edge-crossing width
- Citation
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v.14093, pp.172 - 186
- Indexed
- SCOPUS
- Journal Title
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
- Volume
- 14093
- Start Page
- 172
- End Page
- 186
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/192166
- DOI
- 10.1007/978-3-031-43380-1_13
- ISSN
- 0302-9743
- Abstract
- 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. (WG 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 (Formula presented) either outputs a tree-cut decomposition certifying that the α-edge-crossing width of G is at most (Formula presented) 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.
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