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Thue choosability of trees

2011
*
Discrete Applied Mathematics
*

We prove that for any positive integer ℓ, there is a

doi:10.1016/j.dam.2011.07.017
fatcat:sbt7rdztbjhqlinzhyf3zb5kga
*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. ...##
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The Thue choice number versus the Thue chromatic number of graphs
[article]

2015
*
arXiv
*
pre-print

Recently it was proved that the

arXiv:1508.02559v1
fatcat:ow2hx4xvazgmbjg7p6kthgb63e
*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. ...##
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Page 2096 of Mathematical Reviews Vol. , Issue 88d
[page]

1988
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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’. ...##
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Page 3098 of Mathematical Reviews Vol. , Issue 83h
[page]

1983
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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. ...##
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A coinductive calculus of binary trees

2010
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Information and Computation
*

We study the set T A of infinite binary

doi:10.1016/j.ic.2008.08.006
fatcat:ba6fxt5livh43m3mymp4k2ql64
*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*). ...##
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Behavioural Differential Equations and Coinduction for Binary Trees
[chapter]

2007
*
Lecture Notes in Computer Science
*

We study the set TA of infinite binary

doi:10.1007/978-3-540-73445-1_23
fatcat:6owiptxdkrh45jws5pzbxbdesy
*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 ...##
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Nonrepetitive colorings of trees

2007
*
Discrete Mathematics
*

In this paper we study the

doi:10.1016/j.disc.2006.06.017
fatcat:4d5hizdzs5e77ft6ynwrofzbdm
*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. ...##
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Facial non-repetitive edge-coloring of plane graphs

2010
*
Journal of Graph Theory
*

The bound 4 for

doi:10.1002/jgt.20488
fatcat:f7aqyors5vfe3h5647nhhb6dce
*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*. ...##
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Page 5687 of Mathematical Reviews Vol. , Issue 93j
[page]

1993
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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. ...##
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Some results in square-free and strong square-free edge-colorings of graphs

2007
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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. ...

##
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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? ...##
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A Fast and Accurate Vietnamese Word Segmenter
[article]

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 ==

arXiv:1709.06307v2
fatcat:vn3vqway4neb7aotakzchkutqq
*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." ...##
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THUE: Discovering Top-K High Utility Episodes
[article]

2021
*
arXiv
*
pre-print

In this paper, we propose a novel algorithm, called Top-K High Utility Episode (

arXiv:2106.14830v1
fatcat:w54fk6ewgbgllhitgkuqgthhdi
*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*). ...##
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Max Dehn, Axel Thue, and the Undecidable
[article]

2022
*
arXiv
*
pre-print

This is a short essay on the roles of Max Dehn and Axel

arXiv:1703.09750v5
fatcat:ynx3qkr33vda3dybid2dowa224
*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 ...##
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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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