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Thue choosability of trees

Francesca Fiorenzi, Pascal Ochem, Patrice Ossona de Mendez, Xuding Zhu
2011 Discrete Applied Mathematics  
We prove that for any positive integer ℓ, there is a tree T with π ch (T ) > ℓ.  ...  The Thue choice number of G is the least integer ℓ such that for every ℓ-list assignment L of G, there exists a nonrepetitive L-colouring of G.  ...  So the tree-width of a graph does not provide an upper bound on its Thue choice number. On the other hand, it is easy to show that graphs of bounded tree-depth have bounded Thue choice number.  ... 
doi:10.1016/j.dam.2011.07.017 fatcat:sbt7rdztbjhqlinzhyf3zb5kga

The Thue choice number versus the Thue chromatic number of graphs [article]

Erika Škrabuľáková
2015 arXiv   pre-print
Recently it was proved that the Thue chromatic number and the Thue choice number of the same graph may have an arbitrary large difference in some classes of graphs.  ...  The minimum number of colours in a nonrepetitive vertex colouring of G is the Thue chromatic number π (G).  ...  [11] also showed a result on Thue chromatic number of subdivisions of trees and a result on Thue chromatic number of trees with small radius.  ... 
arXiv:1508.02559v1 fatcat:ow2hx4xvazgmbjg7p6kthgb63e

Page 2096 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Instead, we use the pow- erset of trees; every unknown function symbol, when it has to be ‘interpreted’, is replaced, not by Q, but by the set of all trees.  ...  “The semantic domain we use to define these semantics is no longer the usual set of partial trees, or trees containing the special symbol Q or 1 to represent ‘undefined’.  ... 

Page 3098 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
g€A,h€B and gq is / (the length of a tree) or ¢ (the depth of a tree).  ...  Now observe that a semi-Thue system with 5 productions and undecidable word problem exists and is easily constructible from a Thue system with 3 relations and an undecidable word problem given by Yu.  ... 

A coinductive calculus of binary trees

Alexandra Silva, Jan Rutten
2010 Information and Computation  
We study the set T A of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective.  ...  By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations.  ...  for the thue tree).  ... 
doi:10.1016/j.ic.2008.08.006 fatcat:ba6fxt5livh43m3mymp4k2ql64

Behavioural Differential Equations and Coinduction for Binary Trees [chapter]

Alexandra Silva, Jan Rutten
2007 Lecture Notes in Computer Science  
We study the set TA of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective.  ...  By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations.  ...  The following system of differential equations defines thue: differential equations initial value thue L = thue thue R = thue + one thue(ε) = 0 Note that thue + one equals the (elementwise) complement  ... 
doi:10.1007/978-3-540-73445-1_23 fatcat:6owiptxdkrh45jws5pzbxbdesy

Nonrepetitive colorings of trees

B. Brešar, J. Grytczuk, S. Klavžar, S. Niwczyk, I. Peterin
2007 Discrete Mathematics  
In this paper we study the Thue chromatic number of trees. In view of the fact that (T ) is bounded by 4 in this class we aim to describe the 4-chromatic trees.  ...  The proof relies on Thue sequences with additional properties involving palindromic words. We also investigate nonrepetitive edge colorings of trees.  ...  In fact, all trees with no vertices of degree 2 have the Thue number 4 except the trees that are covered by Lemma 3.2. Theorem 3.4. Let T be a tree in which no vertex is of degree two.  ... 
doi:10.1016/j.disc.2006.06.017 fatcat:4d5hizdzs5e77ft6ynwrofzbdm

Facial non-repetitive edge-coloring of plane graphs

Frédéric Havet, Stanislav Jendrol', Roman Soták, Erika Škrabul'áková
2010 Journal of Graph Theory  
The bound 4 for trees is tight.  ...  We also get better upper bounds for π ′ f (G) in the cases when G is a tree, a plane triangulation, a simple 3-connected plane graph, a hamiltonian plane graph, an outerplanar graph or a Halin graph.  ...  Acknowledgement We are grateful to Igor Fabrici for his stimulating discussion concerning precise value of the facial Thue chromatic index for trees.  ... 
doi:10.1002/jgt.20488 fatcat:f7aqyors5vfe3h5647nhhb6dce

Page 5687 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
sets of trees].  ...  Finally, the authors study limits of derivation sequences of some nonterminat- ing semi-Thue systems by considering equivalent Church-Rosser monadic Thue systems.  ... 

Some results in square-free and strong square-free edge-colorings of graphs

K.S. Sudeep, Sundar Vishwanathan
2007 Discrete Mathematics  
Thue, Über unendliche Zeichenreichen, Norske Vid Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1-22].  ...  Algor. 21 (2002) 336-346] who proved bounds on the minimum number of colors needed for a square-free edge-coloring of G on the class of graphs with bounded maximum degree and trees.  ...  The paper also shows that the Thue number of the Cartesian product of a collection of trees is at most the sum of their individual Thue numbers.  ... 
doi:10.1016/j.disc.2006.09.019 fatcat:cxn6zvmxabgejbvgaadtcxwlgi

Page 984 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
Author summary: “A quadratic regularity test is presented for nondeleting simple deterministic context-free tree grammars as well as for nondeleting macro S grammars.”  ...  (b) The following problem is IT2- hard: instance: a finite Church- Rosser Thue system T; question: is every congruence class of T in 1?  ... 

A Fast and Accurate Vietnamese Word Segmenter [article]

Dat Quoc Nguyen, Dai Quoc Nguyen, Thanh Vu, Mark Dras, Mark Johnson
2017 arXiv   pre-print
Given (s -1 , s +1 ) and the second row in Table 1 , we have a concrete rule "IF Previous-1st-syllable == thuế && Next-1st-syllable == nhập THEN tag = I." SCRDR tree.  ...  For example, given the input raw text "thuế thu nhập cá nhân", the initial segmenter returns the output BI-formed initialized text "thuế/B thu/B nhập/I cá/B nhân/I."  ... 
arXiv:1709.06307v2 fatcat:vn3vqway4neb7aotakzchkutqq

THUE: Discovering Top-K High Utility Episodes [article]

Shicheng Wan, Jiahui Chen, Wensheng Gan, Guoting Chen, Vikram Goyal
2021 arXiv   pre-print
In this paper, we propose a novel algorithm, called Top-K High Utility Episode (THUE) mining within the complex event sequence, which redefines the previous mining task by obtaining the K highest episodes  ...  Finally, the experimental results on both real-life and synthetic datasets reveal that the THUE algorithm can offer six to eight orders of magnitude running time performance improvement over the state-of-the-art  ...  THUE discovers HUEs by spanning the search space with respect to a conceptual lexicographic sequence tree (LS-tree).  ... 
arXiv:2106.14830v1 fatcat:w54fk6ewgbgllhitgkuqgthhdi

Max Dehn, Axel Thue, and the Undecidable [article]

Stefan Müller-Stach
2022 arXiv   pre-print
This is a short essay on the roles of Max Dehn and Axel Thue in the formulation of the word problem for (semi)groups, and the story of the proofs showing that the word problem is undecidable.  ...  It was formulated by Max Dehn for groups in 1911 and, independently, by Axel Thue for general tree structures in 1910 and for semigroups in 1914.  ...  In the 1914 paper, Thue reduced this problem from binary to unary trees, i.e., to words or strings of letters (Zeichenketten) and he introduced (Semi-)Thue systems consisting of a finite set of words a  ... 
arXiv:1703.09750v5 fatcat:ynx3qkr33vda3dybid2dowa224

Page 4316 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
A group having a finite Church-Rosser Thue presentation is proved to be context-free.”  ...  ) and that the converse of a =-rational tree transformation and the composi- tion of any two such tree transformations are L-rational and thus the £-rational tree transformations resemble the rational  ... 
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