Discussiones Mathematicae Graph Theory 29(2) (2009) 219-239
doi: 10.7151/dmgt.1443

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ACYCLIC REDUCIBLE BOUNDS FOR OUTERPLANAR GRAPHS

Mieczysław Borowiecki, Anna Fiedorowicz and Mariusz Hałuszczak

Faculty of Mathematics, Computer Science and Econometrics
University of Zielona Góra
Z. Szafrana 4a, Zielona Góra, Poland

e-mail:M.Borowiecki@wmie.uz.zgora.pl
A.Fiedorowicz@wmie.uz.zgora.pl
M.Hałuszczak@wmie.uz.zgora.pl

Abstract

For a given graph G and a sequence P1, P2,…, Pn of additive hereditary classes of graphs we define an acyclic (P1, P2,…,Pn)-colouring of G as a partition (V1, V2,…,Vn) of the set V(G) of vertices which satisfies the following two conditions:

  1. G[Vi] ∈ Pi for i = 1,…,n,
  2. for every pair i,j of distinct colours the subgraph induced in G by the set of edges uv such that u ∈ Vi and v ∈ Vj is acyclic.

A class R = P1P2 Pn is defined as the set of the graphs having an acyclic (P1, P2,…,Pn)-colouring. If PR, then we say that R is an acyclic reducible bound for P.

In this paper we present acyclic reducible bounds for the class of outerplanar graphs.

Keywords: graph, acyclic colouring, additive hereditary class, outerplanar graph.

2000 Mathematics Subject Classification: 05C75, 05C15, 05C35.

References

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Received 13 December 2007
Revised 4 July 2008
Accepted 23 October 2008