## Abstract Direct proofs of some planarity criteria are presented.
A planarity criterion for cubic bipartite graphs
✍ Scribed by T. Böhme; J. Harant; A. Pruchnewski; I. Schiermeyer
- Book ID
- 108316260
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 719 KB
- Volume
- 191
- Category
- Article
- ISSN
- 0012-365X
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## Butte producxd ihe first example of a 3-connected cubic planar nonhamihonian gJaph. On adding the cxmcition that the graph must he bipartite and admitting 2-connected graphs. We prove that the smallest possible such graph has 26 points and is unique.
The class of 3-connected bipartite cubic graphs is shown to contain a oon-Hamiltonian graph with only 78 vertices and to have a shortness exponent less than one. In this paper, a graph is a simple undirected gaph and a subgraph is an induced subgraph. For a~ay graph G, v(G) denotes the number of ve
Re&ved 4 Fkbruary
In a recent paper, Carsten Thomassen [Carsten Thomassen, Planarity and duality of finite and infinite graphs. J. Combinatorial Theory Ser. B 29 (1980) 244-2711 has shown that a number of criteria for the planarity of a graph can be reduced to that of Kuratowski. Here we present another criterion whi