Abstract
We show that if D is an Eulerian digraph of minimum degree 2k then D has a set S of [1/2k] Euler tours such that each pair of adjacent arcs of D is consecutive in at most one tour of S. We conjecture that our bound of [1/2k] may be improved to k - 2, and obtain some partial results in support of this conjecture.
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References
H. Fleischner, A.J.W. Hilton, B. Jackson, On the maximum number of pairwise compatible euler trails, J. Graph Theory. To appear.
R. Häggkvist, On F-hamiltonian graphs, in: Graph Theory and Related Topics(J.A. Bondy, U.S.R. Murty, eds. ), Academic Press (1979), 219 – 231.
B. Jackson, Compatible Euler tours for transitions systems in eulerian graphs, Discrete Math. 66 (1987), 127 – 131.
A. Kotzig, Problem session, Proc. 10th S.E. Conf. Combinatorics, Graph Theory, Computing, Congr. Numer. XXIV (1979), 914 – 915.
M. Meyniel, Une condition suffisante d’existence d’un circuit hamiltonien dans un graphe orienté, J Combin. Theory Ser. B14 (1973), 137 – 147.
T.W. Tillson, A hamiltonian decomposition of K* 2m , 2m ≥8, J. Combin. Theory Ser. B29 (1980), 68 – 74.
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© 1990 Kluwer Academic Publishers
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Fleischner, H., Jackson, B. (1990). Compatible Euler Tours In Eulerian Digraphs. In: Hahn, G., Sabidussi, G., Woodrow, R.E. (eds) Cycles and Rays. NATO ASI Series, vol 301. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0517-7_9
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DOI: https://doi.org/10.1007/978-94-009-0517-7_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6719-5
Online ISBN: 978-94-009-0517-7
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