Special Classes of Graphs

  • Md. Saidur RahmanEmail author
Part of the Undergraduate Topics in Computer Science book series (UTICS)


In this chapter, we know about some special classes of graphs. Special classes of graphs play important roles in graph algorithmic studies. When we find a computationally hard problem for general graphs, we try to solve those problems for special classes of graphs.

Supplementary material


  1. 1.
    Harary, F.: Graph Theory. Addison-Wesley, Reading, Mass (1972)zbMATHGoogle Scholar
  2. 2.
    Jao, K.F., West, D.B.: Vertex Degrees in Outerplanar Graphs, preprint (2010).
  3. 3.
    Khan, N., Karima, N., Rahman, M.S., Hossain, M.I.: Orthogonal grid pointset embeddings of maximal outerplanar graphs. In: Proceedings of International Conference on Electrical Engineering and Information and Communication Technology (ICEEICT) 2014. IEEE Explore Digital Library (2014)Google Scholar
  4. 4.
    Nishizeki, T., Rahman, M.S.: Planar Graph Drawing. World Scientific, Singapore (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10, 41–51 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Khan, I.K., Rayana, S., Alam, M.J., Rahman, M.S.: On Topological Book Embedding with the Minimum Number of Spine Crossings, Manuscript (2009)Google Scholar
  7. 7.
    Biedl, T., Velasquez, L.E.R.: Drawing planar 3-trees with given face-areas. In: Proceedings of the 17th International Symposium on Graph Drawing (GD 2009), Lecture Notes in Computer Science, vol. 5849, pp. 316–322. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Mondal, D., Nishat, R.I., Rahman, M.S., Alam, M.J.: Minimum-area drawings of plane 3-trees. J. Graph Algorithms Appl. 15(2), 177–204 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Spinrad, J.P.: Efficient Graph Representations. American Mathematical Society, Rhode Island (2003)CrossRefzbMATHGoogle Scholar
  10. 10.
    Dirac, G.A.: On rigid circuit graphs. Anh. Math. Sem. Univ. Hamburg 25, 71–76 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gilmore, P.C., Hoffman, A.J.: A characterization of comparability graphs and of interval graphs. Canadian J. Math. 16, 539548 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Rahman, M.S., Egi, N., Nishizeki, T.: No-bend orthogonal drawings of series-parallel graphs. In: Proceedings of the 13th International Conference on Graph Drawing (GD’05), Lecture Notes in Computer Science, vol. 3843, pp. 409–420. Springer, Heidelberg (2006)Google Scholar
  13. 13.
    Garg, A., Liotta, G.: Almost bend-optimal planar orthogonal drawings of biconnected degree-3 planar graphs in quadratic time. In: Proceedings of Graph Drawing’99. Lecture Notes in Computer Science, vol. 1731, pp. 38–48. Springer, Heidelberg (1999)Google Scholar
  14. 14.
    Di Battista, G., Tamassia, R.: On-line maintenance of triconnected components with SPQR-trees. Algorithmica 15(4), 302–318 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Di Battista, G., Tamassia, R., Vismara, L.: Output-sensetive reporting of disjoint paths. Algorithmica 23, 302–340 (1999)Google Scholar
  16. 16.
    Hossain, M.I., Rahman, M.S.: Straight-line monotone grid drawings of series-parallel graphs. Discret. Math. Alg. Appl. 7(2) (2015)Google Scholar
  17. 17.
    Arnborg, S., Corneil, D., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. Matrix Anal. Appl. 8(2), 277–284 (1987)Google Scholar
  18. 18.
    Bodlaender, H.L.: A tourist guide through treewidth. In: Dassow, J., Kelemenová, A. (eds.) Developments in Theoretical Computer Science (Proc. 7th International Meeting of Young Computer Scientists, Smolenice, 16–20 November 1992), Topics in Computer Mathematics, vol. 6, pp. 1–20. Gordon and Breach (1994)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringBangladesh University of Engineering and Technology (BUET)DhakaBangladesh

Personalised recommendations