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Deeply asymmetric planar graphs. (English) Zbl 1070.05031
Summary: It is proved that by deleting at most 5 edges every planar (simple) graph of order at least 2 can be reduced to a graph having a non-trivial automorphism. Moreover, the bound of 5 edges cannot be lowered to 4.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:
[1] Borodin, O.V., Joint extension of two theorems of kotzig on 3-polytopes, Combinatorica, 13, 121-125, (1993) · Zbl 0777.05050
[2] Erdös, P.; Rényi, A., Asymmetric graphs, Acta math. acad. sci. hungar., 14, 295-315, (1963) · Zbl 0118.18901
[3] Kotzig, A., Contribution to the theory of Eulerian polyhedra, Mat.-fyz. casopis., 5, 101-113, (1955)
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