- Tytuł:
- Generalized Fractional Total Colorings of Complete Graph
- Autorzy:
- Karafová, Gabriela
- Powiązania:
- https://bibliotekanauki.pl/articles/30145422.pdf
- Data publikacji:
- 2013-09-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
fractional coloring
total coloring
complete graphs - Opis:
- An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let $P$ and $Q$ be two additive and hereditary graph properties and let $r,s$ be integers such that $r\geq s$. Then an $\frac{r}{s}$-fractional $(P,Q)$-total coloring of a finite graph $G=(V,E)$ is a mapping $f$, which assigns an $s$-element subset of the set $\{1,2,...,r\}$ to each vertex and each edge, moreover, for any color $i$ all vertices of color $i$ induce a subgraph of property $P$, all edges of color $i$ induce a subgraph of property $Q$ and vertices and incident edges have assigned disjoint sets of colors. The minimum ratio $\frac{r}{s}$ of an $\frac{r}{s}$-fractional $(P,Q)$-total coloring of $G$ is called fractional $(P,Q)$-total chromatic number $\chi_{f,P,Q}^{''}(G)=\frac{r}{s}$. Let $k=$ sup$\{i:K_{i+1}\in P\}$ and $l=$ sup$\{i:K_{i+1}\in Q\}$. We show for a complete graph $K_{n}$ that if $l\geq k+2$ then $\chi_{f,P,Q}^{''}(K_{n})=\frac{n}{k+1}$ for a sufficiently large $n$.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 665-676
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł