- Tytuł:
- Maximum Edge-Colorings Of Graphs
- Autorzy:
-
Jendrol’, Stanislav
Vrbjarová, Michaela - Powiązania:
- https://bibliotekanauki.pl/articles/31341153.pdf
- Data publikacji:
- 2016-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
edge-coloring
r -maximum k -edge-coloring
unique-maximum edge-coloring
weak-odd edge-coloring
weak-even edge-coloring - Opis:
- An $r$-maximum $k$-edge-coloring of $G$ is a $k$-edge-coloring of $G$ having a property that for every vertex $v$ of degree $d_G(v) = d, d \ge r$, the maximum color, that is present at vertex $v$, occurs at $v$ exactly $r$ times. The $r$-maximum index $ \chi_r^′ (G) $ is defined to be the minimum number $k$ of colors needed for an $r$-maximum $k$-edge-coloring of graph $G$. In this paper we show that $ \chi_r^′ (G) \le 3 $ for any nontrivial connected graph $G$ and $ r = 1$ or 2. The bound 3 is tight. All graphs $G$ with $ \chi_1^' (G) =i $, $i = 1, 2, 3$ are characterized. The precise value of the $r$-maximum index, $ r \ge 1 $, is determined for trees and complete graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 117-125
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł