Abstract
A digraph D is supereulerian if D has a spanning eulerian subdigraph. We introduce some sufficient conditions for a digraph D to be supereulerian.
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Algefari, M.J., Alsatami, K.A., Lai, H.-J., Liu, J.: Supereulerian digraphs with given local structures. Inform. Process. Lett 116, 321–326 (2016)
Algefari, M.J., Lai, H.-J.: Supereulerian digraphs with large arc-strong connectivity. J. Graph Theory 81, 393–402 (2016)
Algefari, M.J., Lai, H.-J., Xu, J.: Locally dense supereulerian digraphs. Discret. Appl. Math. 238, 24–31 (2018)
Alsatami, K.A., Zhang, X.D., Liu, J., Lai, H.-J.: On class of supereulerian digraphs. Appl. Math. 7, 320–326 (2016)
Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer-Verlag, London (2009)
Bang-Jensen, J., Maddaloni, A.: Sufficient conditions for a digraph to be supereulerian. J. Graph Theory 79(1), 8–20 (2015)
Boesch, F.T., Suffel, C., Tindell, R.: The spanning subgraphs of eulerian graphs. J. Graph Theory 1, 79–84 (1977)
Bondy, J.A., Murty, U.S.R.: Graph Theory. Springer, New York (2008)
Catlin, P.A.: Supereulerian graphs: a survey. J. Graph Theory 16, 177–196 (1992)
Chen, Z. H., Lai, H.-J.: Reduction techniques for super-Eulerian graphs and related topics-a survey, Combinatorics and graph theory’ 95, Vol. 1 (Hefei), World Sci. Publishing, River Edge, NJ 1995 pp. 53-69
Chvátal, V., Erdős, P.: A note on Hamiltonian circuits. Discret. Math. 2, 111–113 (1972)
Gutin, G.: Cycles and paths in directed graphs. PhD thesis, School of Mathematics, Tel Aviv University (1993)
Gutin, G.: Connected (g; f)-factors and supereulerian digraphs. Ars Combin. 54, 311–317 (2000)
Lai, H.-J., Shao, Y., Yan, H.: An Update on Supereulerian Graphs. WSEAS Trans. Math. 12, 926–940 (2013)
Meyniel, H.: Une condition suffisante d’existence d’un circuit hamiltonien dans un graphe orienté. J. Combin. Theory Ser. B 14, 137–147 (1973)
Pulleyblank, W.R.: A note on graphs spanned by Eulerian graphs. J. Graph Theory 3, 309–310 (1979)
Thomassen, C.: Long cycles in digraphs. Proc. Lond. Math. Soc. (3), 42, 231-251 (1981)
Zhao, L.-C., Meng, J.-H.: A sufficient condition for hamiltonian cycles in digraphs. Ars Combin. 32, 335–338 (1991)
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Algefari, M.J. Degree Condition for a Digraph to be Supereulerian. Graphs and Combinatorics 38, 9 (2022). https://doi.org/10.1007/s00373-021-02421-7
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DOI: https://doi.org/10.1007/s00373-021-02421-7