- Tytuł:
- Generalized Fractional and Circular Total Colorings of Graphs
- Autorzy:
-
Kemnitz, Arnfried
Marangio, Massimiliano
Mihók, Peter
Oravcová, Janka
Soták, Roman - Powiązania:
- https://bibliotekanauki.pl/articles/31339338.pdf
- Data publikacji:
- 2015-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph property
(P,Q)-total coloring
circular coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular (P,Q)- total chromatic number - Opis:
- Let \( \mathcal{P} \) and \( \mathcal{Q} \) be additive and hereditary graph properties, $ r, s \in \mathbb{N}$, $ r \ge s $, and $ [\mathbb{Z}_r]^s $ be the set of all s-element subsets of $\mathbb{Z}_r $. An ($r$, $s$)-fractional (\( \mathcal{P} \),\( \mathcal{Q} \))-total coloring of $G$ is an assignment $ h : V (G) \cup E(G) \rightarrow [\mathbb{Z}_r]^s $ such that for each $ i \in \mathbb{Z}_r $ the following holds: the vertices of $G$ whose color sets contain color $i$ induce a subgraph of $G$ with property \( \mathcal{P} \), edges with color sets containing color $i$ induce a subgraph of $G$ with property \( \mathcal{Q} \), and the color sets of incident vertices and edges are disjoint. If each vertex and edge of $G$ is colored with a set of $s$ consecutive elements of $ \mathbb{Z}_r $ we obtain an ($r$, $s$)-circular (\( \mathcal{P} \),\( \mathcal{Q} \))-total coloring of $G$. In this paper we present basic results on ($r$, $s$)-fractional/circular (\( \mathcal{P} \),\( \mathcal{Q} \))-total colorings. We introduce the fractional and circular (\( \mathcal{P} \),\( \mathcal{Q}\))-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 517-532
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł