Maximum Pagenumber-k Subgraph is NP-Complete
Peter Jonsson, Marco Kuhlmann
TL;DR
This paper proves that finding the largest subgraph embeddable into a k-book with a fixed vertex order is NP-complete for any k greater than or equal to 2, highlighting computational complexity challenges.
Contribution
It establishes the NP-completeness of the Maximum Pagenumber-k Subgraph problem for all k ≥ 2, filling a gap in understanding its computational difficulty.
Findings
NP-complete for k ≥ 2
Complexity results for maximum pagenumber-k subgraph
Implications for graph embedding problems
Abstract
Given a graph with a total order defined on its vertices, the Maximum Pagenumber- Subgraph Problem asks for a maximum subgraph of such that can be embedded into a -book when the vertices are placed on the spine according to the specified total order. We show that this problem is NP-complete for .
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Complexity and Algorithms in Graphs