Dense Arbitrarily Partitionable Graphs
A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . . , Vk) of the vertex set V (G) such that Vi induces a connected subgraph of order ni for i = 1, . . . , k. In...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2016-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1833 |
| Summary: | A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . . , Vk) of the vertex set V (G) such that Vi induces a connected subgraph of order ni for i = 1, . . . , k. In this paper we show that every connected graph G of order n ≥ 22 and with
‖G‖ > (n−42)+12$||G||\; > \;\left( {\matrix{{n - 4} \cr 2 \cr } } \right) + 12$
edges is AP or belongs to few classes of exceptional graphs. |
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| ISSN: | 2083-5892 |