- Tytuł:
- Fall coloring of graphs I
- Autorzy:
-
Balakrishnan, Rangaswami
Kavaskar, T. - Tematy:
-
fall coloring of graphs
non-fall colorable graphs - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/744026.pdf Link otwiera się w nowym oknie
- Opis:
- A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number $χ_f(G)$ of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, $χ(G) ≤ χ_f(G)$. In this paper, we show the existence of an infinite family of graphs G with prescribed values for χ(G) and $χ_f(G)$. We also obtain the smallest non-fall colorable graphs with a given minimum degree δ and determine their number. These answer two of the questions raised by Dunbar et al.
- Dostawca treści:
- Biblioteka Nauki
Artykuł