Geodesic
T-Colorings, Divisibility and the Circular Chromatic Number
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 441-450

Voir la notice de l'article provenant de la source Library of Science

Let T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans esp_T(G) and esp_d⊙T(G), where d is a positive integer and d⊙T={ 0≤t≤d(maxT+1):d|t⇒t/d∈T}. We show that esp_d⊙T(G) = d esp_T(G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = 0 and show that esp_d⊙{0}(G)=⌈d(χ_c(G)-1)⌉, where χ_c(G) is the circular chromatic number of G. This result allows us to formulate several interesting conclusions that include a new formula for the circular chromatic number χ_c(G)=1+inf{esp_d⊙{0}(G)/d:d≥1} and a proof that the formula for the T-edge span of powers of cycles, stated as conjecture in [Y. Zhao, W. He and R. Cao, The edge span of T-coloring on graph C_n^d, Appl. Math. Lett. 19 (2006) 647–651], is true.
Keywords: circular chromatic number, T-coloring 
@article{DMGT_2021_41_2_a6,
     author = {Janczewski, Robert and Trzaskowska, Anna Maria and Turowski, Krzysztof},
     title = {T-Colorings, {Divisibility} and the {Circular} {Chromatic} {Number}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {441--450},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a6/}
}
TY  - JOUR
AU  - Janczewski, Robert
AU  - Trzaskowska, Anna Maria
AU  - Turowski, Krzysztof
TI  - T-Colorings, Divisibility and the Circular Chromatic Number
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2021
SP  - 441
EP  - 450
VL  - 41
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a6/
LA  - en
ID  - DMGT_2021_41_2_a6
ER  - 
%0 Journal Article
%A Janczewski, Robert
%A Trzaskowska, Anna Maria
%A Turowski, Krzysztof
%T T-Colorings, Divisibility and the Circular Chromatic Number
%J Discussiones Mathematicae. Graph Theory
%D 2021
%P 441-450
%V 41
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a6/
%G en
%F DMGT_2021_41_2_a6
Janczewski, Robert; Trzaskowska, Anna Maria; Turowski, Krzysztof. T-Colorings, Divisibility and the Circular Chromatic Number. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 441-450. http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a6/