# Generalized Fractional and Circular Total Colorings of Graphs

Arnfried Kemnitz; Massimiliano Marangio; Peter Mihók; Janka Oravcová; Roman Soták

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 3, page 517-532
- ISSN: 2083-5892

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topArnfried Kemnitz, et al. "Generalized Fractional and Circular Total Colorings of Graphs." Discussiones Mathematicae Graph Theory 35.3 (2015): 517-532. <http://eudml.org/doc/271219>.

@article{ArnfriedKemnitz2015,

abstract = {Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the following holds: the vertices of G whose color sets contain color i induce a subgraph of G with property P, edges with color sets containing color i induce a subgraph of G with property 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 ℤr we obtain an (r, s)-circular (P,Q)-total coloring of G. In this paper we present basic results on (r, s)-fractional/circular (P,Q)-total colorings. We introduce the fractional and circular (P,Q)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.},

author = {Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók, Janka Oravcová, Roman Soták},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph property; (P,Q)-total coloring; circular coloring; fractional coloring; fractional (P,Q)-total chromatic number; circular (P,Q)- total chromatic number.; -total coloring; fractional -total chromatic number; circular -total chromatic number},

language = {eng},

number = {3},

pages = {517-532},

title = {Generalized Fractional and Circular Total Colorings of Graphs},

url = {http://eudml.org/doc/271219},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Arnfried Kemnitz

AU - Massimiliano Marangio

AU - Peter Mihók

AU - Janka Oravcová

AU - Roman Soták

TI - Generalized Fractional and Circular Total Colorings of Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 3

SP - 517

EP - 532

AB - Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the following holds: the vertices of G whose color sets contain color i induce a subgraph of G with property P, edges with color sets containing color i induce a subgraph of G with property 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 ℤr we obtain an (r, s)-circular (P,Q)-total coloring of G. In this paper we present basic results on (r, s)-fractional/circular (P,Q)-total colorings. We introduce the fractional and circular (P,Q)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.

LA - eng

KW - graph property; (P,Q)-total coloring; circular coloring; fractional coloring; fractional (P,Q)-total chromatic number; circular (P,Q)- total chromatic number.; -total coloring; fractional -total chromatic number; circular -total chromatic number

UR - http://eudml.org/doc/271219

ER -

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