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Advanced Algorithmic Graph Theory Course Guide

Explore st-ordering, graph decompositions, representations, and special graph classes with implications. Textbooks and presentation requirements. Presentation and paper schedule included.

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Advanced Algorithmic Graph Theory Course Guide

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  1. u n V t = 16 8 13 V 14 7 12 V 15 11 6 V 10 5 4 9 8 5 V 4 6 3 V 2 V 7 3 2 u u 2 1 s = 1 V 1 21 20 18 19 17 15 12 14 16 11 13 10 9 8 6 7 3 5 4 2 1 CSE 6410 Advanced Algorithmic Graph Theory

  2. Course Contents • Vertex Orderings: st-Numbering and Canonical Orderings; • Graph Decompositions and Their Algorithmic Applications: Ear Decomposition, Canonical Decomposition, Tree Decomposition, Path Width and Tree Width, PQ-tree, SPQR-tree, Split Decomposition, Recursively Decomposable Graphs, Clique Separator Decomposition; .

  3. Course Contents • Graph Representations: Implicit Representations, Intersection and Containment Representations; • Graph Classes Defined by Forbidden Subgraphs; • Graph Classes Defined by Elimination Schemes; Classes of Graphs with Bounded Treewidth and Their Algorithmic Implications; • Characterization, Construction and Recognition Algorithms for Some Special Classes of Graphs.

  4. Text Books • T. Nishizeki and M. S. Rahman, Planar Graph Drawing, World Scientific, Singapore, 2004. • J. P. Spinrad, Efficient Graph Representations, American Mathematical Society, 2003. • Results from Journals

  5. Fundation • M. S. Rahman, Basic Graph Theory, Springer, 2016 (to appear).

  6. Marks Distribution • Attendance 10 • Presentation 15 • Review Paper Writing 15 • Compilation of two class lectures in Latex 10 • Examination 50

  7. Presentation Two Students in a Group Choose a paper on any topic in the course content published in a reputed journal or conference proceedings. Show me the paper and take my approval. You have to read, understand and present the paper. Use PowerPoint /Beamer for presentation.

  8. Presentation Format • Problem definition • Results of the paper • Contribution of the paper in respect to previous results • Algorithms and methodologies including proofs • Future works, open problems and your idea

  9. Presentation Schedule • Presentation time: 20 minutes • Presentation will start from June 5, 2016.

  10. Paper Writing Two Students in a Group Choose a topic from the course content. Write a survey paper for getting at most 85% marks of the item. You need to add some new results to get full marks. Use LaTex for writing the paper. Reporting of Topic: June 26, 2016 (5 min presentation) Submission Deadline of preliminary version: July 31, 2016. Final Submission: September 04, 2016 (A hard copy with all source files in a CD)

  11. Compilation of Class Lectures Each student will compile my class lectures one topic using LaTex (I will assign) . You need to add necessary figures for illustration. Xfig or Latexdraw is recommended for drawing figures.

  12. Thank You

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