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UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN MATHEMATICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)
SYLLABUS
Semester VI - Application Oriented Subject II - Graph Theory II
Planarity; definition and properties, charaterisation of planar graphs, colourability, chromatic number and index, the five colour theorem, four colour problem, chromatic polynomials directed graphs; definition and basic properties, paths and connectedness, digraphs and matrices, tournaments, some application connector problem, shortest path problem, one way traffic system; travelling sales man problem.
[Treatment as in invitation to graph theory by S.Arumugam and S. Ramachandran, chapters 7 (omit 7.3) 8, 9, 10.1 to 10.5]
Matching; Maximal matching, augmenting path, Bergi's theorem, Hall's theorem, Mamage problem, matching and covering; Kongi's minimax theorem, odd and even components, Tuttes theorem.
[chapter 14 in graph theory by S. Kumaravelu and Susheela Kumaravelu]
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