- Tytuł:
- Generalized Fractional Total Colorings of Graphs
- Autorzy:
-
Karafová, Gabriela
Soták, Roman - Powiązania:
- https://bibliotekanauki.pl/articles/31339383.pdf
- Data publikacji:
- 2015-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
fractional coloring
total coloring
automorphism group - Opis:
- Let \( \mathcal{P} \) and \( \mathcal{Q} \) be additive and hereditary graph properties and let $r$, $s$ be integers such that $ r \ge s $. Then an $ r/s$-fractional (\( \mathcal{P} \),\( \mathcal{Q} \))-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 with property \( \mathcal{P} \), all edges of color $i$ induce a subgraph with property \( \mathcal{Q} \) and vertices and incident edges have been assigned disjoint sets of colors. The minimum ratio of an \( \frac{r}{s} \)-fractional (\( \mathcal{P} \),\( \mathcal{Q} \))-total coloring of G is called fractional (\( \mathcal{P} \), \( \mathcal{Q} \))-total chromatic number \( \chi_{f, \mathcal{P} ,\mathcal{Q} }^{ \prime \prime } (G) = \frac{r}{s} \). We show in this paper that \( \chi_{f, \mathcal{P} ,\mathcal{Q} }^{ \prime \prime } \) of a graph \( G \) with \( o(V (G)) \) vertex orbits and \( o(E(G)) \) edge orbits can be found as a solution of a linear program with integer coefficients which consists only of \( o(V (G)) + o(E(G)) \) inequalities.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 463-473
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł