## ON LONG CYCLES THROUGH FOUR PRESCRIBED VERTICES OF A POLYHEDRAL GRAPH

Jochen Harant1,  Stanislav Jendrol'2 and Hansjoachim Walther1

1Institute of Mathematics
Technical University Ilmenau, Germany

2Institute of Mathematics
P.J. Safárik University Košice, Slovakia

## Abstract

For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least [1/36]c+[20/3] through any four vertices of G.

Keywords: graph, long cycle, prescribed vertices.

2000 Mathematics Subject Classification: 05C38.

## References

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