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Minimal unavoidable sets of cycles in plane graphs

Madaras T., Tamasova M.

Opuscula Mathematica

2018

Vol. 38, no. 6

859--870

A set S of cycles is minimal unavoidable in a graph family [formula] if each graph [formula] contains a cycle from S and, for each proper subset S' ⊂ S, there exists an infinite subfamily [formula] such that no graph from [formula] contains a cycle from S'. In this paper, we study minimal unavoidable sets of cycles in plane graphs of minimum degree at least 3 and present several graph constructions which forbid many cycle sets to be unavoidable. We also show the minimality of several small sets consisting of short cycles