3 citations · 3 across the 7 of their papers we have counts for
6 papers · 1 filter
An extension of a cubic 2-connected plane graph G to a hamiltonian plane graph contained in G^{2}
Jan Florek
Let be a simple cubic 2-connected plane graph. For every -factor of having -components there exists a simple hamiltonian plane graph such that $…
Graphs with multi--cycles and the Barnette's conjecture
Jan Florek
Let denote the family of all graphs with multi--cycles and suppose that . Then, is a bipartite graph with a vertex bipartition . We…
Hamiltonian cycles in some family of cubic -connected plane graphs
Jan Florek
Barnette conjectured that all cubic -connected plane graphs with maximum face size at most are hamiltonian. We provide a method of construction of a hamiltonian cycle (in du…
Billiards and the Five Distance Theorem II
Jan Florek
We consider a billiard table rectangle. If a billiard ball is sent out from position F(1) at the angle of , then the ball will rebound against the sides of the rectangle conse…
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…