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Eulerian circuits and path decompositions in quartic planar graphs
A subcycle of an Eulerian circuit is a sequence of edges that are consecutive
in the circuit and form a cycle. We characterise the quartic planar graphs that
admit Eulerian circuits avoiding 3-cycles and 4-cycles. From this, it follows
that a quartic planar graph of order can be decomposed into
many paths with copies of , the path with
edges, if and only if . In particular, every connected
quartic planar graph of even order admits a -decomposition.Comment: 34 pages. Comments welcom