In the mathematical area of graph theory, the Thue number of a graph is a variation of the chromatic index, defined by Alon et al. (2002) and named after mathematician Axel Thue, who studied the squarefree words used to define this number.
Alon et al. define a nonrepetitive coloring of a graph to be an assignment of colors to the edges of the graph, such that there does not exist any even-length simple path in the graph in which the colors of the edges in the first half of the path form the same sequence as the colors of the edges in the second half of the path. The Thue number of a graph is the minimum number of colors needed in any nonrepetitive coloring.[1]
Variations on this concept involving vertex colorings or more general walks on a graph have been studied by several authors including Barát and Varjú, Barát and Wood (2005), Brešar and Klavžar (2004), and Kündgen and Pelsmajer.
theory, the Thuenumber of a graph is a variation of the chromatic index, defined by Alon et al. (2002) and named after mathematician Axel Thue, who studied...
positions of the zero values in the Thue–Morse sequence, and for this reason they have also been called the Thue–Morse set. Non-negative integers that...
{\displaystyle r} is a nonzero rational number. It is named after Axel Thue, who in 1909 proved that a Thue equation can have only finitely many solutions...
Axel Thue (Norwegian: [tʉː]; 19 February 1863 – 7 March 1922) was a Norwegian mathematician, known for his original work in diophantine approximation and...
Goldberg-Seymour Conjecture proposes that this is the largest gap possible. The Thuenumber (a variant of the chromatic index) of the Petersen graph is 5. The Petersen...
token (with n {\displaystyle n} tokens). This number system is used extensively in computing. In the Thue-Morse sequence T {\displaystyle T} , that successively...
2 la(G) matches the bound given by Vizing's theorem. The Thuenumber of a graph is the number of colors required in an edge coloring meeting the stronger...
exponential factorials. The Prouhet–Thue–Morse constant and the related rabbit constant. The Komornik–Loreti constant. Any number for which the digits with respect...
many solutions p/q for every d ≥ 2. In the twentieth century work by Axel Thue, Carl Siegel, and Klaus Roth reduced the exponent in Liouville's work from...
results of analytic number theory that were proved in the period 1900–1950 were in fact ineffective. The main examples were: The Thue–Siegel–Roth theorem...
In number theory, a Liouville number is a real number x {\displaystyle x} with the property that, for every positive integer n {\displaystyle n} , there...
the statement of Thue-Siegel-Roth theorem. Adolf Hurwitz (1891) strengthened this result, proving that for every irrational number α, there are infinitely...
F.; Shallit, Jeffrey; Stoll, Thomas (2011), "Thue–Morse at multiples of an integer", Journal of Number Theory, 131 (8): 1498–1512, arXiv:1009.5357, doi:10...
can all be explicitly calculated and worked with. A breakthrough by Axel Thue and Carl Ludwig Siegel in the twentieth century was the realisation that...
{*}{\underset {R}{\leftrightarrow }}}} is called the Thue congruence generated by R {\displaystyle R} . In a Thue system, i.e. if R {\displaystyle R} is symmetric...
linear combinations of Dirichlet series whose coefficients are terms of the Thue-Morse sequence give rise to identities involving the Riemann Zeta function...
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