DMGT

Discussiones Mathematicae Graph Theory 17(1) (1997) 115-125
DOI: https://doi.org/10.7151/dmgt.1044

THE ORDER OF UNIQUELY PARTITIONABLE GRAPHS

Izak Broere

Department of Mathematics
Rand Afrikaans University
P.O. Box 524, Aucklandpark, 2006 South Africa
e-mail: ib@rau3.rau.ac.za

Marietjie Frick

Department of Mathematics, Applied Mathematics and Astronomy
University of South Africa
P.O. Box 392, Pretoria, 0001 South Africa
e-mail: frickm@alpha.unisa.ac.za

Peter Mihók

Department of Geometry and Algebra
P.J. Šafárik University
Jesenná 5, 041 54 Košice, Slovak Republic
e-mail: mihok@Košice.upjs.sk

Abstract

Let P₁, ..., P_n be properties of graphs. A (P₁, Ľ, P_n)-partition of a graph G is a partition {V₁, ...,V_n} of V(G) such that, for each i = 1,..., n, the subgraph of G induced by V_i has property P_i. If a graph G has a unique (P₁, ..., P_n)-partition we say it is uniquely (P₁, ..., P_n)-partitionable. We establish best lower bounds for the order of uniquely (P₁, ..., P_n)-partitionable graphs, for various choices of P₁, ..., P_n.

Keywords: hereditary property of graphs, uniquely partitionable graphs.

1991 Mathematics Subject Classification: 05C15, 05C70.

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