Deeply asymmetric planar graphs

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Abstract

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.

Keywords

Planar graphs
Asymmetry
Discharging

Cited by (0)

1

The work of this author was supported by Grant 97-01-01075 from the Russian Foundation of Fundamental Research.

2

The work of this author was supported by the program “Universities of Russia—Fundamental Research” (Project Code 1792).

3

The work of these authors was supported by a Grant from INTAS (Project Code 97-1001).

4

The work of this author was supported by Grant 99-01-00581 from the Russian Foundation of Fundamental Research.

5

The work of this author was supported by Grant OPG-7315 from the Natural Sciences and Engineering Research Council of Canada.