Publications in Scientific Journals:
B. Bagheri Gh, T. Feder, H. Fleischner, C. Subi:
"Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture";
Journal of Graph Theory,
We study the existence of hamiltonian cycles in plane cubic graphs 𝐺 having a facial 2-factor . Thus hamiltonicity in 𝐺 is transformed into the existence of a (quasi) spanning tree of faces in the contraction 𝐺∕. In particular, we study the case where 𝐺 is the leapfrog extension (called vertex envelope of a plane cubic graph 𝐺0. As a consequence we prove hamiltonicity in the leapfrog extension of planar cubic cyclically 4-edge-connected bipartite graphs. This and other results of this paper establish partial solutions of Barnette's Conjecture according to which every 3-connected cubic planar bipartite graph is hamiltonian. These results go considerably beyond Goodey's result on this topic.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
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Created from the Publication Database of the Vienna University of Technology.