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THE PERIODIC DOMINO PROBLEM REVISITED
"... NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been m ..."
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made to this work since it was submitted for publication. The definitive version has been published in Theoretical Computer Science, 411:40104016, 2010. doi:10.1016/j.tcs.2010.08.017 Abstract. In this article we give a new proof of the undecidability of the periodic domino problem. The main difference
Twobytwo substitution systems and the undecidability of the domino problem
 of Lecture Notes in Computer Science
, 2008
"... Abstract. Thanks to a careful study of elementary properties of twobytwo substitution systems, we give a complete selfcontained elementary construction of an aperiodic tile set and sketch how to use this tile set to elementary prove the undecidability of the classical Domino Problem. ..."
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Cited by 8 (1 self)
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Abstract. Thanks to a careful study of elementary properties of twobytwo substitution systems, we give a complete selfcontained elementary construction of an aperiodic tile set and sketch how to use this tile set to elementary prove the undecidability of the classical Domino Problem.
The domino problem on groups of polynomial growth. ArXiv eprints
, 2013
"... ABSTRACT. We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov’s theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually free groups, i.e. finite groups, and those having Z as a subgroup of finite index. 1. ..."
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ABSTRACT. We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov’s theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually free groups, i.e. finite groups, and those having Z as a subgroup of finite index. 1.
Dominoes
"... A graph is called a domino if every vertex is contained in at most two maximal cliques. The class of dominoes properly contains the class of line graphs of bipartite graphs, and is in turn properly contained in the class of clawfree graphs. We give some characterizations of this class of graphs, sh ..."
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, show that they can be recognized in linear time, give a linear time algorithm for listing all maximal cliques (which implies a linear time algorithm computing a maximum clique of a domino) and show that the pathwidth problem remains NPcomplete when restricted to the class of chordal dominoes.
Domino treewidth
 DISCRETE MATH. THEOR. COMPUT. SCI
, 1994
"... We consider a special variant of treedecompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino treedecomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck;d such that ..."
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Cited by 87 (4 self)
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is not fixed, this problem is NPcomplete. The domino treewidth problem is hard for the complexity classes W [t] for all t 2 N, and hence the problem for fixed k is unlikely to be solvable in O(n c), where c is a constant, not depending on k.
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