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The Stein theorem for loopless 2-connected plane multigraphs
Jan Florek
Stein proved that for each simple plane triangulation H there exists a partitioning of the vertex of H into two subsets each of which induces a forest if and only if the dual H^{*}…
On Barnette's Conjecture and property
Jan Florek
A conjecture of Barnette states that every 3-connected cubic bipartite plane graph has a Hamilton cycle, which is equivalent to the statement that every simple even plane triangula…
Arc-Disjoint Cycles and Feedback Arc Sets
Jan Florek
Isaak posed the following problem. Suppose is a tournament having a minimum feedback arc set which induces an acyclic digraph with a hamiltonian path. Is it true that the maxim…
Orbits and Hamilton bonds in a family of plane triangulations with vertices of degree three or six
Jan Florek
Let be the family of all 2-connected plane triangulations with vertices of degree three or six. Grünbaum and Motzkin proved (in the dual terms) that every graph $P \in \c…