Decompositions of plane graphs under parity constrains given by faces | Zendy

Július Czap | Zendy; Zsolt Tuza | Zendy

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Decompositions of plane graphs under parity constrains given by faces

Author(s) -

Július Czap,

Zsolt Tuza

Publication year - 2013

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1690

Subject(s) - combinatorics , parity (physics) , edge coloring , graph coloring , mathematics , graph , plane (geometry) , enhanced data rates for gsm evolution , geometry , computer science , physics , graph power , artificial intelligence , line graph , particle physics

An edge coloring of a plane graph G is facially proper if no two faceadjacent 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?

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