@Article{Madaras2018,
author = "Madaras, Tomáš and Tamášová, Martina",
title = "Minimal unavoidable sets of cycles in plane graphs",
journal = "Opuscula Math.",
year = "2018",
volume = "38",
number = "6",
pages = "859--870",
doi = "https://doi.org/10.7494/OpMath.2018.38.6.859",
url = "https://doi.org/10.7494/OpMath.2018.38.6.859",
abstract = "A set \(S\) of cycles is minimal unavoidable in a graph family \(\cal{G}\) if each graph \(G \in \cal{G}\) contains a cycle from \(S\) and, for each proper subset \(S^{\prime}\subset S\), there exists an infinite subfamily \(\cal{G}^{\prime}\subseteq\cal{G}\) such that no graph from \(\cal{G}^{\prime}\) contains a cycle from \(S^{\prime}\). 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.",
keywords = "plane graph, polyhedral graph, set of cycles",
issn = "1232-9274"
}