Minimal unavoidable sets of cycles in plane graphs

Tomáš Madaras, Martina Tamášová
2018 Opuscula Mathematica  
A set S of cycles is minimal unavoidable in a graph family G if each graph G ∈ G contains a cycle from S and, for each proper subset S ⊂ S, there exists an infinite subfamily G ⊆ G such that no graph from G 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.
more » ... sting of short cycles.
doi:10.7494/opmath.2018.38.6.859 fatcat:dy7wud4eonasfcdo4nyrywaequ