TY  - JOUR
ID  - Madaras2018
LB  - Madaras2018
AU  - Madaras, Tomáš
AU  - Tamášová, Martina
TI  - Minimal unavoidable sets of cycles in plane graphs
ST  - Minimal unavoidable sets of cycles in plane graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 6
SP  - 859
EP  - 870
DO  - https://doi.org/10.7494/OpMath.2018.38.6.859
UR  - https://doi.org/10.7494/OpMath.2018.38.6.859
AB  - 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.
KW  - plane graph
KW  - polyhedral graph
KW  - set of cycles
SN  - 1232-9274
ER  -