Access the full text.
Sign up today, get DeepDyve free for 14 days.
Guillaume Ducoffe (2019)
The 4-Steiner Root Problem
D. Rautenbach (2006)
Some remarks about leaf rootsDiscret. Math., 306
E. Eiben, R. Ganian, O-joung Kwon (2016)
A single-exponential fixed-parameter algorithm for Distance-Hereditary Vertex DeletionJ. Comput. Syst. Sci., 97
B. Courcelle, J. Makowsky, Udi Rotics (2000)
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-WidthTheory of Computing Systems, 33
D. Eppstein, Elham Havvaei (2018)
Parameterized Leaf Power Recognition via Embedding into Graph ProductsAlgorithmica, 82
If a vertex of an obstruction has exactly one neighbor w , then w
Jianer Chen, Iyad Kanj, Ge Xia (2010)
Improved upper bounds for vertex coverTheor. Comput. Sci., 411
(i) find k − m (v) + 1 holes H v 1 , . . . , H v k − m (v) + 1 in G (cid:2) v such that V ( H v i ) ∩ V ( H v j ) = { v } for all distinct i , j ∈ { 1 , . . . , k − m (v) + 1 } , or
A. Agrawal, P. Misra, Saket Saurabh, M. Zehavi (2019)
Interval Vertex Deletion Admits a Polynomial Kernel
Eun Kim, O-joung Kwon (2018)
Erdős-Pósa property of chordless cycles and its applications
R4) If G has a true twin-set X of size at least k ` 2, then replace p G, k q with p G z v, k q for any vertex v X
Falk Hüffner, Christian Komusiewicz, Hannes Moser, R. Niedermeier (2010)
Fixed-Parameter Algorithms for Cluster Vertex DeletionTheory of Computing Systems, 47
A. Brandstädt, V. Le (2006)
Structure and linear time recognition of 3-leaf powersInf. Process. Lett., 98
F. Fomin (2010)
Kernelization
M. Dom, Jiong Guo, Falk Hüffner, R. Niedermeier, A. Truß (2006)
Fixed-parameter tractability results for feedback set problems in tournamentsJ. Discrete Algorithms, 8
Eun Kim, O-joung Kwon (2016)
A Polynomial Kernel for Distance-Hereditary Vertex DeletionAlgorithmica, 83
O4) No obstruction H has a cut-vertex v such that H z v has two components having the same number of vertices
E Eiben, R Ganian, O Kwon (2018)
A single-exponential fixed-parameter algorithm for distance-hereditary vertex deletionJ. Comput. System Sci., 97
D. Lokshtanov, N. Narayanaswamy, Venkatesh Raman, M. Ramanujan, Saket Saurabh (2012)
Faster Parameterized Algorithms Using Linear ProgrammingACM Transactions on Algorithms (TALG), 11
3 q P X ˆ t 3 u
M. Dom, Jiong Guo, Falk Hüffner, R. Niedermeier (2006)
Error Compensation in Leaf Power ProblemsAlgorithmica, 44
A. Agrawal, D. Lokshtanov, Umi ReLax, M. Zehavi (2018)
Polylogarithmic Approximation Algorithms for Weighted-F-Deletion Problems*
R. Downey, M. Fellows (2013)
Fundamentals of Parameterized Complexity
B. Courcelle, J. Makowsky, Udi Rotics (1998)
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
B. Jansen, H. Bodlaender (2011)
Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter
Frank Gurski, Egon Wanke (2007)
The Clique-Width of Tree-Power and Leaf-Power Graphs
Marek Cygan, F. Fomin, Lukasz Kowalik, D. Lokshtanov, D. Marx, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh (2015)
Parameterized Algorithms
J. Flum, Martin Grohe (2006)
Parameterized Complexity Theory
H. Bandelt, H. Mulder (1986)
Distance-hereditary graphsJ. Comb. Theory, Ser. B, 41
A. Agrawal, D. Lokshtanov, P. Misra, Saket Saurabh, M. Zehavi (2017)
Feedback Vertex Set Inspired Kernel for Chordal Vertex DeletionACM Transactions on Algorithms (TALG), 15
John Lewis, M. Yannakakis (1980)
The Node-Deletion Problem for Hereditary Properties is NP-CompleteJ. Comput. Syst. Sci., 20
Maw-Shang Chang, Ming-Tat Ko (2007)
The 3-Steiner Root Problem
N Nishimura, P Ragde, DM Thilikos (2002)
On graph powers for leaf-labeled treesJ. Algorithms, 42
V. Bafna, P. Berman, Toshihiro Fujito (1999)
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set ProblemSIAM J. Discret. Math., 12
P. Heggernes, Pim Hof, B. Jansen, Stefan Kratsch, Yngve Villanger (2011)
Parameterized complexity of vertex deletion into perfect graph classes
If Q has a maximal p X ˆ t 1 , 2 , 3 u , k ` 2 q -matching M avoiding some U P Y , then replace p G, k with p G z E p U q
D. Marx (2006)
Chordal Deletion is Fixed-Parameter TractableAlgorithmica, 57
(2010)
Graph theory, volume 173 of Graduate Texts in Mathematics
Yixin Cao, D. Marx (2014)
Chordal Editing is Fixed-Parameter TractableAlgorithmica, 75
Frank Gurski, Egon Wanke (2009)
The NLC-width and clique-width for powers of graphs of bounded tree-widthDiscret. Appl. Math., 157
pt v, w u , 2 q P X ˆ t 2 u and C P Y are adjacent in Q if and only if C has a vertex adjacent to both v and w
Tien-Nam Le, D. Lokshtanov, Saket Saurabh, Stéphan Thomassé, M. Zehavi (2019)
Subquadratic Kernels for Implicit 3-Hitting Set and 3-Set Packing ProblemsACM Transactions on Algorithms (TALG), 15
S. Bessy, C. Paul, Anthony Perez (2008)
Polynomial Kernels for 3-Leaf Power Graph Modification Problems
W. Cunningham (1982)
Decomposition of Directed GraphsSiam Journal on Algebraic and Discrete Methods, 3
v, w
A. Brandstädt, V. Le, R. Sritharan (2008)
Structure and linear-time recognition of 4-leaf powersACM Trans. Algorithms, 5
J. Flum, Martin Grohe (2006)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
B. Jansen, Marcin Pilipczuk (2016)
Approximation and Kernelization for Chordal Vertex Deletion
Manuel Lafond (2021)
Recognizing k-Leaf Powers in Polynomial Time, for Constant kACM Transactions on Algorithms, 19
Diptapriyo Majumdar, Venkatesh Raman, Saket Saurabh (2015)
Kernels for Structural Parameterizations of Vertex Cover - Case of Small Degree Modulators
Sang-il Oum (2005)
Rank-width and vertex-minorsJ. Comb. Theory, Ser. B, 95
S. Bessy, F. Fomin, Serge Gaspers, C. Paul, Anthony Perez, Saket Saurabh, Stéphan Thomassé (2009)
Kernels for feedback arc set in tournamentsJ. Comput. Syst. Sci., 77
P. Heggernes (2016)
Graph-Theoretic Concepts in Computer Science, 9941
M. Lampis (2011)
A kernel of order 2 k-c log k for vertex coverInf. Process. Lett., 111
Eun Kim, O-joung Kwon (2015)
A Polynomial Kernel for Block Graph DeletionAlgorithmica, 79
N. Nishimura, P. Ragde, D. Thilikos (2000)
On Graph Powers for Leaf-Labeled Trees
For a non-negative integer ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document}, the ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document}-leaf power of a tree T is a simple graph G on the leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document}. We provide a polynomial kernel for the problem of deciding whether we can delete at most k vertices to make an input graph a 3-leaf power of some tree. More specifically, we present a polynomial-time algorithm for an input instance (G, k) for the problem to output an equivalent instance (G′,k′)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(G',k')$$\end{document} such that k′⩽k\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k'\leqslant k$$\end{document} and G′\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G'$$\end{document} has at most O(k14)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$O(k^{14})$$\end{document} vertices.
Algorithmica – Springer Journals
Published: Oct 1, 2023
Keywords: ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-Leaf power; Parameterized; Algorithm; Kernelization; Vertex deletion
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.