Generalized Fractional Total Colorings of Graphs

• Autorzy: Gabriela Karafová , Roman Soták
• Języki publikacji: EN

Abstrakty

EN

Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an 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 with property P, all edges of color i induce a subgraph with property Q and vertices and incident edges have been assigned disjoint sets of colors. The minimum ratio of an r/s -fractional (P,Q)-total coloring of G is called fractional (P,Q)-total chromatic number χ″ƒ,P,Q(G) = r/ s . We show in this paper that χ″ƒ,P,Q 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.

Słowa kluczowe

EN

fractional coloring; total coloring; automorphism group.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 3
• Strony: 463-473

Daty

wydano

2015-08-01

otrzymano

2014-04-03

poprawiono

2014-09-03

zaakceptowano

2014-09-03

online

2015-07-29

Twórcy

autor

Gabriela Karafová

• Institute of Mathematics, P. J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia

autor

Roman Soták

• Institute of Mathematics, P. J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1810