Faculty of Mathematics and Computer Science

Convexity in graphs and networks |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Assoc.Prof. TOADERE Teodor, Ph.D., toadere@cs.ubbcluj.ro |

Aims |

To achieve basic knowledges in the domain of convex analysis on metric spaces, finite metric spaces, graphs and networks. The lessons are conceived to be a parallel between the results obtained for graphs in convex analysis and the same theory in networks. |

References |

1. H.-J. Bandelt, Graphs with intrinsec S3 Convexities, J. Graph Theory, 13(2), 1989, 215-228.
2. P.M. Dearing, R.L. Francis, T.J. Lowe, Convex loction problems on tree networks, Oper. Res., 24, 1976, 628-634. 3. P. Duchet, H. Meyniel, Ensemble Convexes dans les Graphes. Theoremes de Helly et de Radon pour Graphes et Surfaces, Europ. J. Combinatorics, 4, 1983, 127-132. 4. M.G. Everett, S.B. Seidman, The hull number of a graph, Disc. Math., 57, 1985, 217-223. 5. M. Farber, R.E. Jamison, Convexity in graphs and hypergraphs, SIAM J. Alg. Disc. Meth., 7, 1986, 433-444. 6. M. Farber, R.E. Jamison, On local convexity in graphs, Disc. Math., 66, 1987, 231-247. 7. M. Gondran, M. Minoux, Graphes et Algorithmes, Eyrolles, Paris, 1979. 8. F. Harary, J. Nieminen, Convexity in graphs, J. Diff. Geom., 16, 1981, 185-190. 9. M.E. Iacob, Convexitate, Aproximare si Optimizare pe Retele, Teza de doctorat, Universitatea Babes-Bolyai, 1997. 10. V.P. Soltan, V.D. Chepoi, Some classes of convex functions in graphs, Dokl. Akad. Nauk. SSSR, 273, 1983, 1314-1317. 11. A. Sochirca, V.P. Soltan, d-Convex functions in graphs, Mat. Issled, 11, 1988, 93-106. 12. V.P. Soltan, Introduction to Axiomatic Convexity Theory, Stiinta, Chisinau, 1984 (rusa). 13. V.P. Soltan Some properties of convex functions I, II, Amer. Math. Transl., 134 (2), 1987, 39-51. 14. V.P. Soltan, Metric convexity in graphs, Studia Univ. Babes-Bolyai Math., XXXVI (4), 1991, 3-43. |

Assessment |

Each student must get two marks: one for the presentation of an essay on a given subject (using a given bibliography) during the semester and the other for an exam at the end of the semester. The final mark is the mean value of the previous two marks. |