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Linear kernels for outbranching problems in sparse digraphs [article]

Marthe Bonamy, Łukasz Kowalik, Michał Pilipczuk, Arkadiusz Socała
2015 arXiv   pre-print
Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k^2) vertices are known on general  ...  In this work we show that k-Leaf Out-Branching admits a kernel with O(k) vertices on H-minor-free graphs, for any fixed family of graphs H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices  ...  Acknowledgments The authors are very grateful to Marcin Pilipczuk for reading the manuscript carefully and providing useful comments.  ... 
arXiv:1509.01675v1 fatcat:23qasdkswrbyjdyfi7dibotk4i

Linear Kernels for Outbranching Problems in Sparse Digraphs

Marthe Bonamy, Łukasz Kowalik, Michał Pilipczuk, Arkadiusz Socała
2016 Algorithmica  
Both these problems have been studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k 2 ) vertices are known on general graphs  ...  In this work we show that k-Leaf Out-Branching admits a kernel with O(k) vertices on H-minor-free graphs, for any fixed family of graphs H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices  ...  Acknowledgements The authors are very grateful to Marcin Pilipczuk for reading the manuscript carefully and providing useful comments.  ... 
doi:10.1007/s00453-016-0244-6 fatcat:gk5iiezflfgnfjdkzex3w35ieu

Directed Nowhere Dense Classes of Graphs [article]

Stephan Kreutzer, Siamak Tazari
2011 arXiv   pre-print
This is of particular interest as these problems are not tractable on any existing digraph measure for sparse classes.  ...  We then study in depth one type of classes of directed graphs which we call nowhere crownful.  ...  first structural property for sparse classes that can successfully be used in the analysis of domination problems on directed graphs.  ... 
arXiv:1104.3808v1 fatcat:pqysgunz6bg3naxkjz53dpj3cm

Editors: Thore Husfeldt and Iyad Kanj

Marthe Bonamy, Łukasz Kowalik, Michał Pilipczuk, Arkadiusz Socała
Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
Although many problems for planar graphs admit kernels of linear size by a general framework of bidimensionality (see [7]), the directed nature of both problems studied here prevents them from satisfying  ...  In this work we are interested in kernelization algorithms for two problems investigated by Dorn et al. [4], namely k-Leaf Out-Branching (LOB) and k-Internal Out-Branching (IOB).  ...  The authors are very grateful to Marcin Pilipczuk for reading the manuscript carefully and providing useful comments.  ... 
fatcat:bhc7ytmgejewfaaa2djv22tdlu

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
The last speaker of the session will chair the session, with two exceptions for PhD-only sessions: Combinatorial Optimization (Mon 18, Room PP, 16-17) chaired by R.  ...  Opening, plenary and closing sessions will take place in the PP amphitheatre. The cocktail event on Tuesday evening will take place in the salle des textiles room, located in Access 3, 1st floor.  ...  We then show a kernelization algorithm for γ-matching parameterized by the size of the solution. Our process produces quadratic kernels.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii