Generalized Fractional and Circular Total Colorings of Graphs

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

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Abstract

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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.

How to cite

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Arnfried 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 -

References

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