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research
Traversing Every Edge in Each Direction Once, But Not at Once: Cubic (Polyhedral) Graphs
Authors
V. R. (Vladimir) Rosenfeld
Publication date
1 January 2017
Publisher
Indonesian Combinatorial Society
Doi
Cite
Abstract
A {\em retracting-free bidirectional circuit} in a graph
G
G
G
is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the opposite direction. Such a circuit revisits each vertex only in a number of steps. Studying the class
Ω
\mathit{\Omega}
Ω
of all graphs admitting at least one retracting-free bidirectional circuit was proposed by Ore (1951) and is by now of practical use to nanotechnology. The latter needs in various molecular polyhedra that are constructed from a single chain molecule in the retracting-free way. Some earlier results for simple graphs, obtained by Thomassen and, then, by other authors, are specially refined by us for a cubic graph
Q
Q
Q
. Most of such refinements depend only on the number
n
n
n
of vertices of
Q
Q
Q
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oai:neliti.com:55255
Last time updated on 19/08/2017
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Last time updated on 13/02/2018