Algorithms for the Strong Chromatic Index of Halin Graphs, Distance-Hereditary Graphs and Maximal Outerplanar Graphs

  • Ton Kloks
  • Sheung-Hung Poon
  • Chin-Ting Ung
  • Yue-Li Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)


We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.


Strong chromatic index Halin graphs Distance-hereditary graphs Outerplanar graphs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andersen, L.: The Strong Chromatic Index of a Cubic Graph Is at Most 10. Discrete Math. 108, 231–252 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bandelt, H., Mulder, H.: Distance-hereditary Graphs. J. Comb. Theory B 41, 182–208 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Cameron, K.: Induced Matchings. Discrete Appl. Math. 24, 97–102 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Cameron, K.: Induced Matchings in Intersection Graphs. Discrete Math. 278, 1–9 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Cameron, K., Sritharan, R., Tang, Y.: Finding a Maximum Induced Matching in Weakly Chordal Graphs. Discrete Math. 266, 133–142 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chang, M., Hsieh, S., Chen, G.: Dynamic Programming on Distance-hereditary Graphs. In: Leong, H.-V., Jain, S., Imai, H. (eds.) ISAAC 1997. LNCS, vol. 1350, pp. 344–353. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Corneil, D., Perl, Y., Stewart, L.: A Linear Recognition Algorithm for Cographs. SIAM J. Comput. 14, 926–934 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Dvořák, Z., Král, D.: Classes of Graphs with Small Rank Decompositions Are χ-bounded. Manuscript on ArXiv: 1107.2161.v1 (2011).Google Scholar
  9. 9.
    Fomin, F., Golovach, P.A., Lokshtanov, D., Saurabh, S.: On the Price of Generality. In: Proceedings of the 20th Annual-SIAM Symposium on Discrete Algorithms, pp. 825–834 (2009)Google Scholar
  10. 10.
    Ganian, R., Hliněný, P.: Better Polynomial Algorithms on Graphs of Bounded Rank-Width. In: Fiala, J., Kratochvíl, J., Miller, M. (eds.) IWOCA 2009. LNCS, vol. 5874, pp. 266–277. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Halin, R.: Studies on Minimally n-connected Graphs. In: Welsh, D. (ed.) Combinatorial Mathematics and its Applications, pp. 129–136. Academic Press, London (1971)Google Scholar
  12. 12.
    Hayward, R., Spinrad, J., Sritharan, R.: Improved Algorithms for Weakly Chordal Graphs. ACM Trans. Alg. 3, 1549–6325 (2007)MathSciNetGoogle Scholar
  13. 13.
    Howorka, E.: A Characterization of Distance-hereditary Graphs. Q. J. Math. 28, 417–420 (1977)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Kloks, T.: Treewidth – Computations and Approximations. LNCS, vol. 842. Springer, Heidelberg (1994)zbMATHCrossRefGoogle Scholar
  15. 15.
    Lai, H., Lih, K., Tsai, P.: The Strong Chromatic Index of Halin Graphs. Discrete Math. 312, 1536–1541 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Laskar, R., Shier, D.: On Powers and Centers of Chordal Graphs. Discrete Appl. Math. 6, 139–147 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Lih, K., Liu, D.: On the Strong Chromatic Index of Cubic Halin Graphs. Appl. Math. Lett. 25, 898–901 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Molloy, M., Reed, B.: A Bound on the Strong Chromatic Index of a Graph. J. Comb. Theory B. 69, 103–109 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Moser, M., Sikdar, S.: The Parameterized Complexity of the Induced Matching Problem in Planar Graphs. Discrete Appl. Math. 157, 715–727 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Salavatipour, M.: A Polynomial Algorithm for Strong Edge Coloring of Partial k-trees. Discrete Appl. Math. 143, 285–291 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Shiu, W., Lam, P., Tam, W.: On Strong Chromatic Index of Halin Graphs. J. Comb. Math. Comb. Comput. 57, 211–222 (2006)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Shiu, W., Tam, W.: The Strong Chromatic Index of Complete Cubic Halin Graphs. Appl. Math. Lett. 22, 754–758 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Wolk, E.: A Note on “The Comparability Graph of a Tree”. In: Proceedings of the American Mathematical Society, vol. 16, pp. 17–20 (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ton Kloks
    • 1
  • Sheung-Hung Poon
    • 1
  • Chin-Ting Ung
    • 1
  • Yue-Li Wang
    • 2
  1. 1.Department of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Department of Information ManagementNational Taiwan University of Science and TechnologyTaipeiTaiwan

Personalised recommendations