# Generalized Fractional Total Colorings of Complete Graph

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 4, page 665-676
- ISSN: 2083-5892

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topGabriela Karafová. "Generalized Fractional Total Colorings of Complete Graph." Discussiones Mathematicae Graph Theory 33.4 (2013): 665-676. <http://eudml.org/doc/267837>.

@article{GabrielaKarafová2013,

abstract = {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 ≥ s Then an [...] 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 [...] of an [...] - fractional (P,Q)-total coloring of G is called fractional (P,Q)-total chromatic number X″f,P,Q(G) = [...] Let k = sup\{i : Ki+1 ∈ P\} and l = sup\{i Ki+1 ∈ Q\}. We show for a complete graph Kn that if l ≥ k +2 then \_X″f,P,Q(Kn) = [...] for a sufficiently large n.},

author = {Gabriela Karafová},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {fractional coloring; total coloring; complete graphs},

language = {eng},

number = {4},

pages = {665-676},

title = {Generalized Fractional Total Colorings of Complete Graph},

url = {http://eudml.org/doc/267837},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Gabriela Karafová

TI - Generalized Fractional Total Colorings of Complete Graph

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 4

SP - 665

EP - 676

AB - 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 ≥ s Then an [...] 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 [...] of an [...] - fractional (P,Q)-total coloring of G is called fractional (P,Q)-total chromatic number X″f,P,Q(G) = [...] Let k = sup{i : Ki+1 ∈ P} and l = sup{i Ki+1 ∈ Q}. We show for a complete graph Kn that if l ≥ k +2 then _X″f,P,Q(Kn) = [...] for a sufficiently large n.

LA - eng

KW - fractional coloring; total coloring; complete graphs

UR - http://eudml.org/doc/267837

ER -

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