- Tytuł:
- A note on cyclic chromatic number
- Autorzy:
- Zlámalová, Jana
- Powiązania:
- https://bibliotekanauki.pl/articles/744549.pdf
- Data publikacji:
- 2010
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
plane graph
cyclic colouring
cyclic chromatic number - Opis:
- A cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number $χ_c(G)$ of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 conjectured that $χ_c(G) ≤ Δ* + 2$ for any 3-connected plane graph G with maximum face degree Δ*. It is known that the conjecture holds true for Δ* ≤ 4 and Δ* ≥ 18. The validity of the conjecture is proved in the paper for some special classes of planar graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2010, 30, 1; 115-122
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł