1 research outputs found
Minimal unavoidable sets of cycles in plane graphs
A set of cycles is minimal unavoidable in a graph family if each graph contains a cycle from and, for each proper subset , there exists an infinite subfamily such that no graph from contains a cycle from . 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