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The Cartographer
Anti-Path Cover on Sparse Graph Classes
December 15, 2016 Β· Declared Dead Β· π Doctoral Workshop on Mathematical and Engineering Methods in Computer Science
"No code URL or promise found in abstract"
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Authors
Pavel DvoΕΓ‘k, DuΕ‘an Knop, TomΓ‘Ε‘ MasaΕΓk
arXiv ID
1612.04985
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.DM
Citations
4
Venue
Doctoral Workshop on Mathematical and Engineering Methods in Computer Science
Last Checked
4 months ago
Abstract
We show that it is possible to use Bondy-Chvatal closure to design an FPT algorithm that decides whether or not it is possible to cover vertices of an input graph by at most k vertex disjoint paths in the complement of the input graph. More precisely, we show that if a graph has tree-width at most w and its complement is closed under Bondy-Chvatal closure, then it is possible to bound neighborhood diversity of the complement by a function of w only. A simpler proof where tree-depth is used instead of tree-width is also presented.
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