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characterization; $k$-tree; $K_t$-minor

References:

[1] Bodlaender, H. L.: **A partial $k$-arboretum of graphs with bounded treewidth**. Theor. Comput. Sci. 209 (1998), 1-45. DOI 10.1016/S0304-3975(97)00228-4 | MR 1647486 | Zbl 0912.68148

[2] Bose, P., Dujmović, V., Krizanc, D., Langerman, S., Morin, P., Wood, D. R., Wuhrer, S.: **A characterization of the degree sequences of 2-trees**. J. Graph Theory 58 (2008), 191-209. DOI 10.1002/jgt.20302 | MR 2419516 | Zbl 1167.05308

[3] Cai, L.: **On spanning 2-trees in a graph**. Discrete Appl. Math. 74 (1997), 203-216. DOI 10.1016/S0166-218X(96)00045-5 | MR 1444941 | Zbl 0883.05040

[4] Reed, B. A.: **Algorithmic aspects of treewidth**. Recent Advances in Algorithms and Combinatorics CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Vol. 11 Springer, New York 85-107 (2003). MR 1952980