Locally-cyclic graphs covering complete tripartite graphs.

*(English)*Zbl 0761.05038A graph is locally cyclic if for each vertex the subgraph induced by its neighbors is a cycle. Such a graph has the property that every edge is in exactly two triangles. Moreover, if you place a 2-cell on each triangle the result is that the graph is embedded on a 2-dimensional manifold.

In this paper the author begins with a triangular embedding of the regular complete tripartite graph and, using a voltage assignment, derives locally-cyclic covering graphs. These graphs have the property that the number of triangles divided by the genus of the surface is asymptotically 4, and so they are extremal in this sense.

In this paper the author begins with a triangular embedding of the regular complete tripartite graph and, using a voltage assignment, derives locally-cyclic covering graphs. These graphs have the property that the number of triangles divided by the genus of the surface is asymptotically 4, and so they are extremal in this sense.

Reviewer: D.S.Archdeacon (Burlington)

##### MSC:

05C10 | Planar graphs; geometric and topological aspects of graph theory |

05C35 | Extremal problems in graph theory |

##### Keywords:

locally-cyclic graphs; complete tripartite graphs; clean triangulations; voltages; embedding; genus
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##### References:

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