7,330 research outputs found
Topological entropy of transitive dendrite maps
We show that every dendrite satisfying the condition that no subtree of it
contains all free arcs admits a transitive, even exactly Devaney chaotic map
with arbitrarily small entropy. This gives a partial answer to a question of
Baldwin from 2001.Comment: 26 pages, 4 figure
Hamiltonicity of 3-arc graphs
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple of
vertices such that both and are paths of length two. The
3-arc graph of a graph is defined to have vertices the arcs of such
that two arcs are adjacent if and only if is a 3-arc of
. In this paper we prove that any connected 3-arc graph is Hamiltonian, and
all iterative 3-arc graphs of any connected graph of minimum degree at least
three are Hamiltonian. As a consequence we obtain that if a vertex-transitive
graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of
degree at least three, then it is Hamiltonian. This confirms the well known
conjecture, that all vertex-transitive graphs with finitely many exceptions are
Hamiltonian, for a large family of vertex-transitive graphs. We also prove that
if a graph with at least four vertices is Hamilton-connected, then so are its
iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201
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