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On graphical partitions and planarity

✍ Scribed by E.J. Farrell

Book ID
103058867
Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
630 KB
Volume
18
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

ChvBtal gave a necessary condition for a partition to have a planar realization. It is of interest to find: (i) partitions which satisfy the condition of the theorem but have no planar realization. and also (ii) partitions which satisfy the condition and have only p:!anar realizations. We give a list of all such partitions with 6, 7, 8 and 9 elements. We atso give an algorithm for generating all graphs with a given pditiorr, an algorithm for generating ail s&compositions of a given composition and some general classes of partitions which have planar realizations only and some which have non-planar realizations only.

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