Geodesic
Spanning Trees with Disjoint Dominating and 2-Dominating Sets
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 299-308.

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In this paper, we provide a structural characterization of graphs having a spanning tree with disjoint dominating and 2-dominating sets.
Keywords: domination, 2-domination, spanning tree 
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Miotk, Mateusz; Żyliński, Paweł. Spanning Trees with Disjoint Dominating and 2-Dominating Sets. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 299-308. http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a18/

[1] V. Anusuya and R. Kala, A note on disjoint dominating sets in graphs, Int. J. Contem. Math. Sci. 7 (2012) 2099–2110.

[2] H. Broersma, O. Koppius, H. Tuinstra, A. Huck, T. Kloks, D. Kratsch and H. Müller, Degree-preserving trees, Networks 35 (2000) 26–39. https://doi.org/10.1002/(SICI)1097-0037(200001)35:1¡26::AID-NET3¿3.0.CO;2-M

[3] F. Buckley and M. Lewinter, On graphs with center-preserving spanning tree, Graph Theory Notes N.Y. 14 (1987) 33–35.

[4] F. Buckley and M. Lewinter, A note on graphs with diameter-preserving spanning trees, J. Graph Theory 12 (1988) 525–528. https://doi.org/10.1002/jgt.3190120408

[5] F. Buckley and Z. Palka, Property preserving spanning trees in random graphs, in: Random Graphs ’87, Karoński, Jaworski and Ruciński (Ed(s)), (Wiley & Sons, New York, 1990) 17–28.

[6] L. Cai and D.G. Corneil, Tree spanners, SIAM J. Discrete Math. 8 (1995) 359–387. https://doi.org/10.1137/S0895480192237403

[7] G. Chartrand, L. Lesniak and P. Zhang, Graphs and Digraphs (CRC Press, Boca Raton, 2016).

[8] P. Delgado, W.J. Desormeaux and T.W. Haynes, Partitioning the vertices of a graph into two total dominating sets, Quaest. Math. 39 (2016) 863–873. https://doi.org/10.2989/16073606.2016.1188862

[9] W.J. Desormeaux, T.W. Haynes and M.A. Henning, Partitioning the vertices of a cubic graph into two total dominating sets, Discrete Appl. Math. 223 (2017) 52–63. https://doi.org/10.1016/j.dam.2017.01.032

[10] S. Földes and P.L. Hammer, Split graphs, Congr. Numer. 19 (1977) 311–315.

[11] M.A. Henning, Ch. Löwenstein and D. Rautenbach, Remarks about disjoint dominating sets, Discrete Math. 309 (2009) 6451–6458. https://doi.org/10.1016/j.disc.2009.06.017

[12] M.A. Henning and D.F. Rall, On graphs with disjoint dominating and 2-dominating sets, Discuss. Math. Graph Theory 33 (2013) 139–146. https://doi.org/10.7151/dmgt.1652

[13] A. Kaneko and K. Yoshimoto, On spanning trees with restricted degrees, Inform. Process. Lett. 73 (2000) 163–165. https://doi.org/10.1016/S0020-0190(00)00018-1

[14] Ch.-Ch. Lin, G.J. Chang and G.-H. Chen, The degree-preserving spanning tree problem in strongly chordal and directed path graphs, Networks 56 (2009) 183–187. https://doi.org/10.1002/net.20359

[15] Y. Liu and J. Huang, Diameter-preserving spanning trees in sparse weighted graphs, Graphs Combin. 25 (2009) 753–758. https://doi.org/10.1007/s00373-010-0887-z

[16] M. Miotk, J. Topp and P. Żyliński, Disjoint dominating and 2-dominating sets in graphs, Discrete Optim. 35 (2020) 100553. https://doi.org/10.1016/j.disopt.2019.100553

[17] I. Papoutsakis, Tree spanners of bounded degree graphs, Discrete Appl. Math. 236 (2018) 395–407. https://doi.org/10.1016/j.dam.2017.10.025

[18] J. Southey and M.A. Henning, A characterization of graphs with disjoint dominating and paired-dominating sets, J. Comb. Optim. 22 (2011) 217–234. https://doi.org/10.1007/s10878-009-9274-1

[19] J. Southey and M.A. Henning, Dominating and total dominating partitions in cubic graphs, Cent. Eur. J. Math. 9 (2011) 699–708. https://doi.org/10.2478/s11533-011-0014-2