Chartrand and Harary have shown that if G is a non-outerplanar graph such that, for every edge e, both the deletion G \ e and the contraction G/e of e from G are outerplanar, then G is isomorphic to K4 or K2,3. An a-outerplanar graph is a graph which is not outerplanar such that, for some edge a , b
A generalization of outerplanar graphs
✍ Scribed by L. Oubiña; R. Zucchello
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 898 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
l[Rt G be a planar graph and W a set of vertices, G is W-outerplanar if it can be embedded in the plane so that all vertices of W lie on the exterior face. We give a characterization of these graphs by forbidden subgraphs, an upper bound on the number of edges, and other properties which lead to an algorithm of W-outerplanarity testing.
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An outerplanar graph is one that can be embedded in the plane so that all of the vertices lie on one of the faces. We investigate a conjecture of Chartrand, Geller, and Hedetniemi, that every planar graph can be edge-partitioned into two outerplanar subgraphs. We refute the stronger statement that e