### Abstract

An edge coloring of a plane graph G is facially proper if no two face-adjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?

Original language | English |
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Pages (from-to) | 521-530 |

Number of pages | 10 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 33 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

- Edge coloring
- Parity partition
- Plane graph

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

**Decompositions of plane graphs under parity constrains given by faces.** / Czap, Július; Tuza, Z.

Research output: Contribution to journal › Article

*Discussiones Mathematicae - Graph Theory*, vol. 33, no. 3, pp. 521-530. https://doi.org/10.7151/dmgt.1690

}

TY - JOUR

T1 - Decompositions of plane graphs under parity constrains given by faces

AU - Czap, Július

AU - Tuza, Z.

PY - 2013

Y1 - 2013

N2 - An edge coloring of a plane graph G is facially proper if no two face-adjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?

AB - An edge coloring of a plane graph G is facially proper if no two face-adjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?

KW - Edge coloring

KW - Parity partition

KW - Plane graph

UR - http://www.scopus.com/inward/record.url?scp=84882311185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882311185&partnerID=8YFLogxK

U2 - 10.7151/dmgt.1690

DO - 10.7151/dmgt.1690

M3 - Article

AN - SCOPUS:84882311185

VL - 33

SP - 521

EP - 530

JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

SN - 1234-3099

IS - 3

ER -