Speaker
Prof.
Tomaž Pisanski
(University of Primorska and University of Ljubljana)
Description
By shrinking a one-factor F in a cubic graph G an associated quartic graph
X = G/F is obtained. This construction arose recently in at least two unrelated
contexts. On the one hand the search for Hamilton cycles in G is related to the search of
some special sub quartic Eulerian subgraphs W of X. On the other hand
it was shown by Potočnik, Spiga and Verret that certain cubic vertex-transitive
graphs G are closely related to the associated arc-transitive quartic graphs X.
The reverse construction that yields a cubic graph G with a one-factor F from
a quartic graph X is possible, if it is known how the four arcs incident in each
vertex of X are partitioned into two pairs. For instance, this is the case when X
is equipped with a two-factorization. In turn, this property arising from the fundamental
partition of certain graph bundles was recently used by Bonvicini and the author
to classify Hamiltonian I-graphs.
Primary author
Prof.
Tomaž Pisanski
(University of Primorska and University of Ljubljana)
