Welcome to the homepage of

Dr.T.KARTHICK

      Indian Statistical Institute, Chennai Centre      

    110, Nelson Manickam Road, Aminjikarai    

   Chennai-600029, INDIA    



    Education:   M.Sc., M.Phil., Ph.D.

    Specialization:   Graph Theory, Graph Algorithms and Combinatorics.

    Areas of Interest:
    Graph classes. Graph colorings and its variations.  Perfect graphs and its generalizations.
    Structure/decomposition of graphs.   Domination.   Independent sets. Algorithmic aspects in graphs.
    Current Research:
  • Bounds for χ in terms of ω, and Reed's conjecture.

  • Algorithmic aspects in vertex coloring.

  • Bounds for equitable/star coloring.

  • Independent/Stable set problem in graph classes.

  • Efficient domination in graph classes.
    Ph.D. Thesis:
  • T.Karthick, Vertex coloring and cliques of certain P6-free graphs and claw-free graphs.
    Indian Institute of Technology Madras (2010).
    Edited Volumes:
  • Andreas M.Hinz, S.Arumugam, R.Balakrishnan, S.Francis Raj, T.Karthick, K.Somasundaram, Xuding Zhu,
    Special Issue of International Conference on Graph Theory and its Applications (ICGTA 2015).
    Electronic Notes in Discrete Mathematics, Volume 53 (2016).
    List of Publications:
  • T.Karthick, F.Maffray and Lucas Pastor, Polynomial cases for the vertex coloring problem.
    Submitted for publication. Available on arXiv.

  • T.Karthick and Suchismita Mishra, Chromatic bounds for some classes of 2K2-free graphs.
    Submitted for publication. Available on arXiv.

  • T.Karthick and F.Maffray, Coloring (gem, co-gem)-free graphs.
    Submitted for publication.

  • T.Karthick, Star Coloring of certain graph classes.
    Revised version submitted for publication.

  • T.Karthick and Suchismita Mishra, Coloring (P6,diamond,K4)-free graphs.
    Accepted for publication. Under revision. Available on arXiv.

  • T.Karthick, Independent sets in some classes of Si,j,k-free graphs.
    Journal of Combinatorial Optimization, 34(2) (2017) 612-630.

  • A.Brandstädt, E.M.Eschen, E.Friese and T.Karthick, Efficient domination for classes of P6-free graphs.
    Discrete Applied Mathematics, 223 (2017) 15-27.

  • T.Karthick and F.Maffray, Maximum weight independent sets in classes related to claw-free graphs.
    Discrete Applied Mathematics, 216 (2017) 232-239.

  • T.Karthick, Structure of squares and efficient domination in graph classes.
    Theoretical Computer Science, 652 (2016) 38-46.

  • T.Karthick and F.Maffray, Maximum weight independent sets in (S1,1,3,bull)-free graphs.
    In:COCOON 2016, Lecture Notes in Computer Science, 9797 (2016) pp.385-392.

  • T.Karthick and F.Maffray, Vizing Bound for the chromatic number on some graph classes.
    Graphs and Combinatorics, 32(4) (2016) 1447-1460.

  • T.Karthick, Independent sets in classes related to chair-free graphs.
    In:CALDAM 2016, Lecture Notes in Computer Science, 9602 (2016) pp.224-232.

  • T.Karthick and F.Maffray, Weighted independent sets in classes of P6-free graphs.
    In: Proc. of 9th International Colloquium on Graph Theory and Combinatorics (ICGT 2014), France.
    Discrete Applied Mathematics, 209 (2016) 217-226.

  • A.Brandstädt and T.Karthick, Weighted efficient domination in two subclasses of P6-free graphs.
    Discrete Applied Mathematics, 201 (2016) 38-46.

  • T.Karthick, Weighted independent sets in a subclass of P6-free graphs.
    Discrete Mathematics, 339 (2016) 1412-1418.

  • T.Karthick, Star chromatic bounds.
    In:ICGTA 2015, Electronic Notes in Discrete Mathematics, 53 (2016) 413-419.

  • T.Karthick, New polynomial case for efficient domination in P6-free graphs.
    In:CALDAM 2015, Lecture Notes in Computer Science, 8959 (2015) pp.81-88.

  • T.Karthick, Note on equitable coloring of graphs.
    Australasian Journal of Combinatorics, 59(2) (2014) 251-259.

  • T.Karthick, On atomic structure of P5-free subclasses and maximum weight independent set problem.
    Theoretical Computer Science, 516 (2014) 78-85.

  • T.Karthick and C.R.Subramanian, Star coloring of subcubic graphs.
    Discussiones Mathematicae Graph Theory, 33 (2013) 373-385.

  • M.Basavaraju, L.S.Chandran and T.Karthick, Maximum weight independent sets in hole- and dart-free graphs.
    Discrete Applied Mathematics, 160 (2012) 2364-2369.

  • T.Karthick and F.Maffray, A characterization of claw-free b-perfect graphs.
    Discrete Mathematics, 312 (2012) 324-330.

  • N.R.Aravind, T.Karthick and C.R.Subramanian, Bounding χ in terms of ω and Δ for some classes of graphs.
    Discrete Mathematics, 311 (2011) 911-920.

  • S.A.Choudum and T.Karthick, Maximal cliques in {P2∪P3,C4}-free graphs.
    Discrete Mathematics, 310 (2010) 3398-3403.

  • S.A.Choudum and T.Karthick, First-fit coloring of {P5,K4-e}-free graphs.
    Discrete Applied Mathematics, 158 (2010) 620-626.

  • S.A.Choudum, T.Karthick and M.A.Shalu, Linear chromatic bounds for a subfamily of 3K1-free graphs.
    Graphs and Combinatorics, 24(4) (2008) 413-428.

  • S.A.Choudum, T.Karthick and M.A.Shalu, Perfect coloring and linearly χ-bound P6-free graphs.
    Journal of Graph Theory, 54(4) (2007) 293-306.
    Manuscripts:
  • F.Bonomo, S.A.Choudum and T.Karthick, On b-perfect graph conjecture and forbidden subgraphs.
    Presented in "8th French Combinatorial Conference (2010)", France.
    "International Workshop on Graph Theory and its Applications (2010)", Trichy, India.