منابع مشابه
On uniquely partitionable planar graphs
Let ~1,22 . . . . . ~,; n/>2 be any properties of graphs. A vertex (~L, ~2 . . . . . J~,,)-partition of a graph G is a partition (V1, l~,...,/7,,) of V(G) such that for each i = 1,2 . . . . . n the induced subgraph G[Vi] has the property ~i. A graph G is said to be uniquely (~1,~2 . . . . . ~,)-partitionable if G has unique vertex (2~1, ~2 , . . . , ~,)-partition. In the present paper we invest...
متن کاملRemarks on the existence of uniquely partitionable planar graphs
We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 ”to be a forest”.
متن کاملUniquely partitionable graphs
Let P1, . . . ,Pn be properties of graphs. A (P1, . . . ,Pn)-partition of a graph G is a partition of the vertex set V (G) into subsets V1, . . . , Vn such that the subgraph G[Vi] induced by Vi has property Pi; i = 1, . . . , n. A graph G is said to be uniquely (P1, . . . ,Pn)-partitionable if G has exactly one (P1, . . . ,Pn)-partition. A property P is called hereditary if every subgraph of ev...
متن کاملThe order of uniquely partitionable graphs
Let P1, . . . ,Pn be properties of graphs. A (P1, . . . ,Pn)-partition of a graph G is a partition {V1, . . . , Vn} of V (G) such that, for each i = 1, . . . , n, the subgraph of G induced by Vi has property Pi. If a graph G has a unique (P1, . . . ,Pn)-partition we say it is uniquely (P1, . . . ,Pn)partitionable. We establish best lower bounds for the order of uniquely (P1, . . . ,Pn)-partitio...
متن کاملUniquely partitionable planar graphs with respect to properties having a forbidden tree
Let P1, P2 be graph properties. A vertex (P1,P2)-partition of a graph G is a partition {V1, V2} of V (G) such that for i = 1, 2 the induced subgraph G[Vi] has the property Pi. A property R = P1◦P2 is defined to be the set of all graphs having a vertex (P1,P2)-partition. A graph G ∈ P1◦P2 is said to be uniquely (P1,P2)-partitionable if G has exactly one vertex (P1,P2)-partition. In this note, we...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00102-2