List Hcoloring a graph by removing few vertices
Chitnis, Rajesh and Egri, László and Marx, Dániel (2013) List Hcoloring a graph by removing few vertices. In: Algorithms – ESA 2013 21st Annual European Symposium, Sophia Antipolis, France, September 24, 2013. Proceedings. Lecture Notes in Computer Science (8125). SpringerVerlag Wien, Berlin, pp. 313324. ISBN 9783642404498 10.1007/9783642404504_27

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Abstract
In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v) ⊆ V(H) for each vertex v ∈ V(G), and an integer k. The task is to decide whether there exists a set W ⊆ V(G) of size at most k such that there is a homomorphism from G \ W to H respecting the lists. We show that DLHom(H), parameterized by k and H, is fixedparameter tractable for any (P6,C 6)free bipartite graph H; already for this restricted class of graphs, the problem generalizes Vertex Cover, Odd Cycle Transversal, and Vertex Multiway Cut parameterized by the size of the cutset and the number of terminals. We conjecture that DLHom( H ) is fixedparameter tractable for the class of graphs H for which the list homomorphism problem (without deletions) is polynomialtime solvable; by a result of Feder et al. [9], a graph H belongs to this class precisely if it is a bipartite graph whose complement is a circular arc graph. We show that this conjecture is equivalent to the fixedparameter tractability of a single fairly natural satisfiability problem, Clause Deletion ChainSAT. © 2013 SpringerVerlag.
Item Type:  Book Section 

Subjects:  Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány 
Divisions:  Informatics Laboratory 
SWORD Depositor:  MTMT Injector 
Depositing User:  MTMT Injector 
Date Deposited:  07 Feb 2018 07:00 
Last Modified:  21 Jul 2019 13:45 
URI:  http://eprints.sztaki.hu/id/eprint/9350 
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