Working Seminar in Discrete
Mathematics
Tentative Schedule
Meeting 2-2:50pm on Mondays in
UC 425
1.
August
29th: (Scott Bailey) Matroids and the Tutte Polynomial, the
color Tutte polynomial and its relation to the Kauffman bracket and the Jones
polynomial.
Some relevant papers:
"A contribution to the theory of chromatic polynomials", W.T. Tutte (Canadian J. Math. 6, 1954, p. 80-91) http://math.ca/cjm/v6/cjm1954v06.0080-0091.pdf
"A Tutte polynomial for signed graphs", L. Kauffman (Discrete Applied Mathematics 25, 1989, p. 105-127)
"Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width", J.A. Makowsky
"The multivariate Tutte polynomial
(alias Potts model) for graphs and matroids", A.D. Sokal
2.
September 12th: (Scott Bailey) Computations involving the Tutte
polynomial.
3.
September 19th: (Christian Barrientos) Roman Domination.
4. September 26th: (Christian Barrientos) Roman Domination.
5. October 3rd: (Christian Barrientos) Roman Domination part 2.
6. October
10th: (Elliot Krop) Vizing’s Conjecture—part 1.
An excellent survey paper:
http://www.imfm.si/preprinti/PDF/01099.pdf
7.
October
17th: (Elliot Krop) Vizing’s Conjecture—part 2.
8. October 24th: (Group) We discuss the new result of Goncalves, et al. on the domination number of grid graphs.
Their paper may be downloaded from ArXiv here: http://arxiv.org/PS_cache/arxiv/pdf/1102/1102.5206v1.pdf
8.
October
31st: (Christopher Raridan) Top graph labelings and problems.
The
preeminent dynamic survey:
http://www.combinatorics.org/Surveys/ds6.pdf
9.
November
7th: (Christian Barrientos) Matroids.
10.
November
14th: (Michael Dancs) Partition theory—part 1 (introduction).
11.
Next: (Michael Dancs) Partition theory—part 2 (generating
functions).
12.
Next: (Elliot Krop/Christian Barrientos) The probabilistic method in
combinatorics.
See N. Alon and J.H. Spencer, “The Probabilistic Method in Combinatorics”
13.
Next:
(Elliot Krop/Christian Barrientos) The probabilistic
method in combinatorics.