Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. If G has at least one (F,H)-WORM coloring, then W−F,H(G) denotes the minimum number of colors in an (F,H)-WORM coloring of G. We show that (a) W−F,H(G) ≤ 2 if |V (F)| ≥ 3 and H contains a cycle, (b) W−F,H(G) ≤ 3 if |V (F)| ≥ 4 and H is a forest with Δ (H) ≥ 3, (c) W−F,H(G) ≤ 4 if |V (F)| ≥ 5 and H is a forest with 1 ≤ Δ (H) ≤ 2. The cases when both F and H are nontrivial paths are more complicated; therefore we consider a relaxation of the original problem. Among others, we prove that any 3-connected plane graph (respectively outerplane graph) admits a 2-coloring such that no facial path on five (respectively four) vertices is monochromatic.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
353-368
Opis fizyczny
Daty
wydano
2017-05-01
otrzymano
2015-12-03
poprawiono
2016-01-22
zaakceptowano
2016-02-22
online
2017-04-01
Twórcy
autor
- Department of Applied Mathematics and Business Informatics Faculty of Economics, Technical University of Košice Němcovej 32, 040 01 Košice,, julius.czap@tuke.sk
autor
- Institute of Mathematics, P.J. Šafárik University Jesenná 5, 040 01 Košice,, stanislav.jendrol@upjs.sk
autor
- Institute of Mathematics, P.J. Šafárik University Jesenná 5, 040 01 Košice,, juraj.valiska@student.upjs.sk
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1921