Discussiones
Mathematicae Graph Theory 19(1) (1999) 71-78
DOI: https://doi.org/10.7151/dmgt.1086
UNIQUELY PARTITIONABLE PLANAR GRAPHS WITH RESPECT TO PROPERTIES HAVING A FORBIDDEN TREE
Jozef Bucko Department of Mathematics, Technical University |
Jaroslav Ivančo Department of Geometry and Algebra |
Abstract
Let P1, P2 be graph properties. A vertex (P1,P2)-partition of a graph G is a partition { V1,V 2} of V(G) such that for i = 1,2 the induced subgraph G[Vi] has the property Pi. A property ℜ = P1 ºP2 is defined to be the set of all graphs having a vertex (P1,P2)-partition. A graph G ∈ P1ºP2 is said to be uniquely (P1,P2)-partitionable if G has exactly one vertex (P1,P2)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree.
Keywords: uniquely partitionable planar graphs, forbidden graphs.
1991 Mathematics Subject Classification: 05C15, 05C70.
References
[1] | J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043. |
[2] | J. Bucko, P. Mihók and M. Voigt, Uniquely partitionable planar graphs, Discrete Math. 191 (1998) 149-158, doi: 10.1016/S0012-365X(98)00102-2. |
[3] | M. Borowiecki, J. Bucko, P. Mihók, Z. Tuza and M. Voigt, Remarks on the existence of uniquely partitionable planar graphs, 13. Workshop on Discrete Optimization, Burg, abstract, 1998. |
[4] | P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58. |
Received 14 July 1998
Revised 24 November 1998
Close