2trees.bbl
\begin{thebibliography}{10}

\bibitem{MR556007}
Lowell~W. Beineke and Edward~F. Schmeichel.
\newblock Degrees and cycles in graphs.
\newblock In {\em Proc. of the 2nd International Conference on Combinatorial
  Mathematics}, volume 319 of {\em Ann. New York Acad. Sci.}, pages 64--70.
  1979.

\bibitem{TB05}
T{\"u}rker B{\i}y{\i}ko{\u{g}}lu.
\newblock Degree sequences of {H}alin graphs, and forcibly cograph-graphic
  sequences.
\newblock {\em Ars Combinatoria}, 75, 2005.

\bibitem{Bodlaender-TCS98}
Hans~L. Bodlaender.
\newblock A partial $k$-arboretum of graphs with bounded treewidth.
\newblock {\em Theoret. Comput. Sci.}, 209(1-2):1--45, 1998.

\bibitem{MR1761726}
Mao-cheng Cai, Xiaotie Deng, and Wenan Zang.
\newblock Solution to a problem on degree sequences of graphs.
\newblock {\em Discrete Math.}, 219(1-3):253--257, 2000.

\bibitem{VC}
Va{\v{s}}ek Chv{\'a}tal.
\newblock Planarity of graphs with given degrees of vertices.
\newblock {\em Nieuw Arch. Wisk.}, 3(17):47--60, 1969.

\bibitem{clr01}
Thomas~H. Cormen, Charles~E. Leiserson, Ronald~L. Rivest, and Clifford Stein.
\newblock {\em Introduction to algorithms}.
\newblock MIT Press, Cambridge, U.S.A., second edition, 2001.

\bibitem{MR654585}
Richard~A. Duke and Peter~M. Winkler.
\newblock Degree sets of {$k$}-trees: small {$k$}.
\newblock {\em Israel J. Math.}, 40(3-4):296--306, 1981.

\bibitem{MR725887}
Richard~A. Duke and Peter~M. Winkler.
\newblock Realizability of almost all degree sets by {$k$}-trees.
\newblock In {\em Proc. of the 13th Southeastern {C}onference on
  {C}ombinatorics, {G}raph {T}heory and {C}omputing}, volume~35 of {\em Congr.
  Numer.}, pages 261--273, 1982.

\bibitem{MR703138}
Richard~A. Duke and Peter~M. Winkler.
\newblock Degree sets of {$k$}-trees: small degrees.
\newblock {\em Utilitas Math.}, 23:177--200, 1983.

\bibitem{EG}
Paul Erd{\H{o}}s and Tibor Gallai.
\newblock Graphs with prescribed degrees of vertices.
\newblock {\em Mat. Lapok}, 11:264--274, 1960.

\bibitem{MR621898}
Stefano Fanelli.
\newblock An unresolved conjecture on nonmaximal planar graphical sequences.
\newblock {\em Discrete Math.}, 36(1):109--112, 1981.

\bibitem{MR0148049}
S.~Louis Hakimi.
\newblock On realizability of a set of integers as degrees of the vertices of a
  linear graph. {I}.
\newblock {\em J. Soc. Indust. Appl. Math.}, 10:496--506, 1962.

\bibitem{MR0469802}
S.~Louis Hakimi and Edward~F. Schmeichel.
\newblock On planar graphical degree sequences.
\newblock {\em SIAM J. Appl. Math.}, 32(3):598--609, 1977.

\bibitem{HS81}
Peter~L. Hammer and Bruno Simeone.
\newblock The splittance of a graph.
\newblock {\em Combinatorica}, 1:275--284, 1981.

\bibitem{MR0089165}
V{\'a}clav Havel.
\newblock Eine {B}emerkung \"uber die {E}xistenz der endlichen {G}raphen.
\newblock {\em \v Casopis P\v est. Mat.}, 80:477--480, 1955.

\bibitem{MR1750983}
Qing~Long Hu.
\newblock On the planar realization of maximal {E}uler {$3$}-sequences {$(d\sb
  p=4)$}.
\newblock {\em Sichuan Shifan Daxue Xuebao Ziran Kexue Ban}, 22(6):641--645,
  1999.

\bibitem{KPW77}
Shashi~F. Kapoor, Albert~.D. Polimeni, and Curtiss~E. Wall.
\newblock Degree sets for graphs.
\newblock {\em Fund. Math.}, 95:183--194, 1977.

\bibitem{MR1204564}
De~Ying Li and Jing~Zhong Mao.
\newblock Degree sequences of maximal outerplanar graphs.
\newblock {\em J. Central China Normal Univ. Natur. Sci.}, 26(3):270--273,
  1992.

\bibitem{cocoon-2trees}
Zvi Lotker, Debapriyo Majumdar, N.S. Narayanaswamy, and Ingmar Weber.
\newblock Sequences characterizing $k$-trees.
\newblock In {\em Proc. of the 12th Annual International Computing and
  Combinatorics Conference (COCOON'06)}, Lecture Notes in Computer Science.
  Springer.
\newblock to appear.

\bibitem{MR1975945}
Russell Merris.
\newblock Split graphs.
\newblock {\em European J. Combin.}, 24(4):413--430, 2003.

\bibitem{MR655641}
A.~Ramachandra~Rao.
\newblock Degree sequences of cacti.
\newblock In {\em Combinatorics and graph theory}, volume 885 of {\em Lecture
  Notes in Math.}, pages 410--416. Springer, Berlin, 1981.

\bibitem{MR1952984}
Bruce~A. Reed.
\newblock Algorithmic aspects of tree width.
\newblock In {\em Recent advances in algorithms and combinatorics}, volume~11
  of {\em {CMS} {B}ooks in {M}athematics/{O}uvrages de {M}ath\'ematiques de la
  {SMC}}, pages 85--107. Springer, 2003.

\bibitem{MR681928}
Peter~M. Winkler.
\newblock Graphic characterization of {$k$}-trees.
\newblock In {\em Proceedings of the 12th Southeastern Conference on
  Combinatorics, Graph Theory and Computing}, volume~33 of {\em Congr. Numer.},
  pages 349--357, 1981.

\bibitem{MR703601}
Peter~M. Winkler.
\newblock Existence of graphs with a given set of {$r$}-neighborhoods.
\newblock {\em J. Combin. Theory Ser. B}, 34(2):165--176, 1983.

\end{thebibliography}
