- Tytuł:
- T-Colorings, Divisibility and the Circular Chromatic Number
- Autorzy:
-
Janczewski, Robert
Trzaskowska, Anna Maria
Turowski, Krzysztof - Powiązania:
- https://bibliotekanauki.pl/articles/32083881.pdf
- Data publikacji:
- 2021-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
circular chromatic number
T-coloring - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 441-450
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł