- Professor, also Associate member of Computer Science Department
- Member of UBC Vancouver Senate, Joint Faculties, 2008-2017
- Background:
- B.Math., Waterloo (1976)
- Ph.D., Caltech (1980)
- NSERC PDF, Waterloo (1980-1982)
- NSERC URF, Waterloo (1982-1984)
- Office Location: Mathematics Annex, 1114
- Office Telephone: (604) 822-6105
- Email Address: anstee at math dot ubc dot ca
- Department Telephone: (604) 822-2666; Fax: (604) 822-6074

Math 184 Section 201 (Jan, 2014)

Math 443 Section 101 (Sept, 2013)

Math 441 Section 201 (Sept, 2014)

Math 223 Section 102 (Sept, 2014)

Math 340 Section 202 (Jan, 2012)

Math 523 Section 201 (Jan , 2011)

Math 104 Section 103 (Sept, 2006)

Various bits of Information (advice) for undergraduates is at the bottom of this page. I am currently the advior for students in the Dual Degree program combining a B.Sc. with a B.Ed. In this role I am the person selecting eligible students (from the Mathematics side) and providing guidance during their time in the program. I may be able to help other students with other issues if you contact me.

Tim Chan (USRA 2001)

Nima Kamoosi (USRA 2002)

Balin Fleming (USRA 2003)

Chris Ryan (USRA 2004)

Laura Dunwoody (USRA 2005)

Robert Tseng (USRA 2006)

Farzin Barekat (NSERC RA 2007)

Steven Karp (USRA 2008)

Jonathan Blackman (USRA 2009)

Connor Meehan (USRA 2010)

Ronnie Chen (USRA 2011)

Ron Estrin (USRA 2012)

Foster Tom (USRA 2013)

Maxwell Allman (USRA 2014)

Hangjun (Gavin) Yang MSc 2005

Miguel Raggi Ph.D. 2011 Thesis (August 2011)

Christina Koch MSc 2013 Thesis (April 2013)

Discrete Mathematics, Extremal Set Theory, Graph Theory, Matching Theory

Matching theory is an important foundational topic in combinatorial optimization. An optimal degree constrained subgraph of a given graph is sought. The simplest case seeks to match vertices in pairs. I have obtained efficient strongly polynomial algorithms using the fact that fractional degree constrained subgraphs can easily be obtained via network flows. I have obtained some simplified existence theorems this way which have been useful in some graph decomposition problems of a design theory nature. I have explored (with Tank Aldred, Jonathan Blackman, Steve Locke, Robert Tseng, Gavin (Hangjun) Yang) the extent to which certain graphs are robust with respect to the property of having a perfect matching under vertex deletion. Of course not all vertex deletions are allowable such as the need to delete an even number of vertices, avoiding deleting all neighbours of a vertex and, if the graph is bipartite, deleting the same number of vertices from each part.

I have considered some extremal problems of the following type. Given a family of subsets of a set of size

Graph theory is a central area in combinatorics. A variety of problems are considered such as examining the structure of certain classes of graphs. With Martin Farber results were obtained concerning the class of bridged graphs. These are graphs which contain no cycle of length greater than three as an isometric subgraph. With J. Pryzytcki and D. Rolfsen, results of Tutte on rotors in graphs and chromatic polynomials were extended to mutations of knots and knot polynominals. Fast algorithms for determining diameter critical graphs using Fast Matrix multiplication were developed.

The following download of code written by Miguel Raggi FConfThesisVersion.tar.gz contains the Ph.D. thesis version of program that accepts as input an integer k and a configuration (or a set of configurations) and determines what is missing on k rows in a matrix avoiding the given configuration(s). This software has been helpful in proving a number of results but is not expected to work for k greater than 6.

The following Java applet was written by Nima Kamoosi (NSERC USRA summer 2002) to display the shattered sets associated with a set system. I have difficulty getting it to run on all systems; it was written with Java 2.

Various Old (Beamer) Talks. More recent talks below.

Forbidden Submatrices SIAM Discrete Mathematics Conference, Halifax, June 19, 2012. (pdf file)

Student Research U of South Carolina, February 26, 2013. (pdf file)

Critical Substructures SIAM SEAS, U of Tennessee, March 23, 2013. (pdf file)

Forbidden Families of Configurations AMS, U of Iowa, Ames IA, April 28, 2013. (pdf file)

Forbidden Families of Configurations St. John's Newfoundland, June 13, 2013. (pdf file)

Large Forbidden Configurations Minneapolis, June 17, 2014. (pdf file)

Forbidden Configurations: A shattered history Combinatorial Potlatch, University of Western Washington, November 22, 2014. (pdf file)

Math Circle talk On the Quest for the Perfect Square January 26, 2015. (pdf file)

- R.P. Anstee, Linyuan Lu, Multicoloured Families of Forbidden Configurations. (arKiv 1409.4123) submitted to J. Comb. Th. Ser A., 16pp Sep 29, 2014 (pdf file)
- R.P. Anstee, A. Sali, Large Forbidden Configurations and Design Theory, submitted to Studia. Sci. Math. Hung., 9pp Sept 15 2014 (pdf file)
- R.P. Anstee, F. Barekat, Design Theory and Some Non-simple Forbidden Configurations , submitted to Journal of Combinatorial Designs, 27pp. (pdf file)
- R.P. Anstee, J. Madden, Finding d-critical spanning subgraphs, preprint, 10pp.
- R.P. Anstee, Some problems concerning forbidden configurations, preprint, 10pp. (pdf file)
- R.P. Anstee, Yunsun Nam, Included and Excluded edges for regular factors.

- R.P. Anstee, Linyuan Lu, Repeated columns and an old chestnut,
*Elec. J. of Combinatorics*, 20(2013), issue 4, P2, 11pp (pdf file) (arXiv 1305.0603) - R.P. Anstee, C.L. Koch, Forbidden Families of Configurations,
*Australasian J. of Combinatorics*, accepted Nov 2013. 18pp (pdf file) (arXiv 1307.1148) - R.P. Anstee, C. Koch, M. Raggi, A, Sali, Forbidden Configurations and Product Constructions,
*Graphs and Combinatorics*, 6(2014), 1325-1349. (pdf file) - R.P. Anstee, M. Raggi, A, Sali, Forbidden Configurations: Boundary Cases,
*European J. Combin.*,**35**(2014), 51-66. (pdf file) - R.P. Anstee, A survey of forbidden configuration results,
*Elec. J. of Combinatorics*,**20**(2013), DS20, 56pp. (pdf file) - R.P. Anstee, R. Chen, Forbidden Submatrices, some new bounds and constructions,
*Elec. J. of Combinatorics*,**20**(2013), P5, 13pp. (pdf file) - R.P. Anstee, M. Raggi, A, Sali, Evidence for a Forbidden Configuration Conjecture; one more case solved,
*Discrete Math.***312**(2012), pp. 2720-2729 - R.P. Anstee, M. Raggi, Genetic Algorithms applied to problems of Forbidden Configurations ,
*Elec. J. of Combinatorics*,**18**(2011), P230, 23pp. (pdf file) - R.P. Anstee, J. Blackman, H. Yang, Perfect matchings in grid graphs after vertex deletions,
*SIAM J of Discrete Mathematics*,**25**(2011), 1754-1767. - R.P. Anstee, Balin Fleming, Linear Algebra Methods for Forbidden Configurations,
*Combinatorica*,**31**(2011) 1-19. - R.P. Anstee, C.G.W. Meehan, Forbidden Configurations and Repeated Induction, Discrete Math., 311(2011), 2187-2197.
- R.P. Anstee, F. Barekat, A. Sali, Small Forbidden Configurations V: Exact Bounds for 4x2 cases,
*Studia Sci. Math. Hun.*,**48**(2011), 1-22. - R.P. Anstee, Balin Fleming, Two Refinements of the Bound of Sauer, Perles and Shelah, and Vapnik and Chevonenkis,
*Discrete Math.*,**310**(2010), 3318-3323. - R.P. Anstee, S.N. Karp, Forbidden Configurations: Exact bounds determined by critical substructures,
*Elec. J. of Combinatorics*,**17**(2010), R50, 27pp. - R.E.L.
Aldred, R.P. Anstee, S.C. Locke, Perfect matchings after vertex deletions,
*Discrete Math.***307**(2007), 3048-3054. - R.P. Anstee, N. Kamoosi, Small Forbidden Configurations III,
*Elec. J. Combin.***14**(2007), R79, (34pp). - R.P.
Anstee, A. Sali, Latin Squares and Low Discrepancy Allocation of two-dimensional data,
*European J. of Combin.***28**(2007), 2115-2124. - R.P. Anstee, Peter Keevash, Pairwise intersections and forbidden configurations,
*European J. of Combin.***27**(2006), 1235-1248. - R.P. Anstee, B. Fleming, Z. Furedi, and A. Sali, Color critical hypergraphs and forbidden configurations, proceedings of EuroComb 2005, Berlin, Germany.
*Discrete mathematics and Theoretical Computer Science,*2005, 117-122. - R.P.
Anstee, A. Sali, Small Forbidden Configurations IV,
*Combinatorica*,**25**(2005), 503-518. - R.P.
Anstee, R. Ferguson, J.R. Griggs, Circular Permutations with low
discrepancy k-sums,
*J. of Combinatorial Theory (A)*,**100**(2002), 302-321. - R.P.
Anstee, L. Ronyai, A. Sali, Shattering News,
*Graphs and Combinatorics*,**18**(2002),59-73. - R.P.
Anstee, R. Ferguson, A. Sali, Small Forbidden Configurations II,
*Electronic Journal of Combinatorics*Vol**8**(1), 2001, R4(25pp). - R.P.
Anstee, J. Demetrovics, G.O.H. Katona, A. Sali, Low Discrepancy Allocation
of Two Dimensional Data, in
*Foundations of Information and Knowledge Systems*, Proceedings of 1st FoIKS, Burg, Germany, Lecture Notes in Computer Science, v**1762**, Springer, 2000, 1-12.

(This has been referred to in US patent 6513100, System and Method for Fast Referencing a Reference counted item.) - R.P.
Anstee, On a Conjecture Concerning Forbidden Submatrices,
*J. Combin. Math and Combin. Comp.***32**(2000), 185-192. - R.P.
Anstee, V. Rumchev, Asymptotic Reachable Sets for Discrete-Time Positive
Linear Systems,
*Systems Science***25**(1999), 41-48. - R.P.
Anstee, Yunsun Nam: Convexity of Degree Sequences,
*J. Graph Theory,***30**(1999), 147-156. - R.P.
Anstee, Yunsun Nam: More Sufficient Conditions for a graph to have
factors,
*Discrete Math.***184**(1998), 15-24. - R.P.
Anstee, L. Caccetta: Orthogonal Matchings,
*Discrete Math.***179**(1998), 37-47. - R.P.
Anstee, L. Caccetta: Recognizing Diameter Critical Graphs, in
*Combinatorics, Complexity and Logic: Proceedings of Discrete Mathematics and Theory of Computer Science '96,*Springer, 1997, 105-112. - R.P.
Anstee, J.R. Griggs and A. Sali: Small Forbidden Configurations
*Graphs and Combinatorics,***13**(1997), 97-118. - R.P.
Anstee, A. Sali: Sperner families of bounded VC-dimension,
*Discrete Math.***175**(1997), 13-21. - R.P.
Anstee: Dividing a graph by degrees,
*J. Graph Theory,***23**(1996), 377-384. - R.P.
Anstee, J.R. Griggs: An application of Matching Theory to edge colourings,
*Discrete Math.***156**(1996), 253-256. - R.P.
Anstee: Forbidden Configurations: Induction and Linear Algebra,
*European J. Of Combin.***16**(1995), 427-438. - R.E.L.
Aldred, R.P. Anstee: On the density of sets of divisors,
*Discrete Math.***137**(1995), 345-349. - R.P.
Anstee: Minimum vertex weighted deficiency of (g,f)-factors,
*Discrete Appl. Math.***44**(1993), 247-260. - R.P.
Anstee: Matching Theory: Fractional to Integral,
*N.Z. J. of Math.***21**(1992), 17-32. - R.P.
Anstee: Simplified Existence Theorems for (g,f)-factors,
*Discrete Appl. Math.***27**(1990), 29-38. - R.P.
Anstee: Forbidden Configurations, determinants and discrepancy,
*European J. of Combin.***11**(1990), 15-19. - R.P.
Anstee, J.H. Przytycki and D. Rolfsen: Knot Polynomials and generalized
mutation,
*Topology and its Applics.***32**(1989), 237-249. - R.P.
Anstee: A Forbidden Configuration Theorem of Alon,''
*J. of Combinatorial Theory***Ser.A 47**(1988), 16-27. - R.P.
Anstee, M. Farber: On Bridged Graphs and Cop-win Graphs,
*J. of Combinatorial Theory (B)***44**(1988), 22-28. - R.P.
Anstee: A Polynomial Algorithm for
*b*-Matching: An Alternative Approach,''*Information Processing Letters***24**(1987), 153-157. - R.P.
Anstee, Z. Furedi: Forbidden Submatrices,
*Discrete Math***62**(1986), 225-243. - R.P.
Anstee: Invariant Sets of Arcs in Network Flow Problems,
*Discrete Applied Math.***13**(1986), 1-7. - R.P.
Anstee: General Forbidden Configuration Theorems,
*J. of Combinatorial Theory (A)***40**(1985), 108-124. - R.P.
Anstee, U.S.R. Murty: Matrices with Forbidden Subconfigurations,
*Discrete Math.***54**(1985), 113-116. - R.P.
Anstee: An Algorithmic Proof of Tutte's f-factor Theorem,
*J. of Algorithms***6**(1985), 112-131. - R.P.
Anstee, M. Farber: Characterizations of Totally Balanced Matrices,
*J. of Algorithms***5**(1984), 215-230. - R.P.
Anstee, Hypergraphs with no special cycles,
*Combinatorica***3**(1983), 141-146. - R.P.
Anstee, The Network Flows approach for matrices with given row and column
sums,
*Discrete Math.***44**(1983), 125-138. - R.P.
Anstee, Extensions of the notion of conformality in hypergraphs,
*Congressus Numerantium***39**(1983), 82-88. - R.P.
Anstee, Properties of a class of (0,1)-matrices covering a given matrix,
*Can. J. Math.***34**(1982), 438-453. - R.P.
Anstee, Triangular (0,1)-matrices with prescribed row and column sums,
*Discrete Math.***40**(1982), 1-10. - R.P.
Anstee, Properties of (0,1)-matrices without certain configurations,
*J. of Combinatorial Theory (A)***31**(1981), 256-269. - R.P.
Anstee, Properties of (0,1)-matrices with no triangles,
*J. of Combinatorial Theory (A)***29**(1980), 186-198. - R.P.
Anstee, Marshall Hall Jr., John G. Thompson, Planes of Order 10 do not
have a collineation of order 5,
*J. of Combinatorial Theory (A)***29**(1980), 39-58. - R.P.
Anstee, An analogue of group divisible designs for Moore Graphs,
*J. of Combinatorial Theory (B)***30**(1980), 11-20. - R.P.
Anstee, Properties of (0,1)-matrices with forbidden configurations,
Proceedings of Joint Canada-France Combinatorial Colloquium,
*Annals of Discrete Math.***9**(1980), 177-179.

Some links for pursuing teaching

A collection of advising documents

Web page for Math Information Session March 2011

My informal advice for graduating students who are interested in graduate school.

Careers blurb; some ideas about the many directions students have pursued.

A blog with pictures from Keramic Studio magazine; a hobby of mine.