Welcome to the Home Page of James Oxley
Name: James Oxley
Position: Alumni Professor of Mathematics
Publications in pdf format.
Teaching:
Fall, 2009. Math 7001-01. Communicating Mathematics I TuTh 3:00 - 5:00. Lockett 241.
Here is the course syllabus.
Here is a guide for writing a teaching statement.
Office Hours: Fall, 2009. TuTh 11:00-12:00 and by appointment.
Research interests:
Matroid theory and graph theory. Here is an introduction to matroid theory entitled "What is a matroid?", in Postscript format and in pdf format. This paper is a revision of a paper that appeared in Cubo 5 (2003), 179-218. It contains some new material, including some exercises, along with updates of some results from the original paper. It was prepared for presentation at the Workshop on Combinatorics and its Applications run by the New Zealand Institute of Mathematics and its Applications in Auckland in July, 2004.
A second edition of my book [Matroid Theory, Oxford University Press, New York, 1992] is currently in preparation. This will be a major revision of the book. Here is a file containing an errata and update on conjectures, problems, and references from the first edition of the book in pdf format and in Postscript format. In July, 2006, the first edition of the book was reprinted with corrections in a paperback version available through Oxford University Press in the USA and in the UK and Europe. This version of the book incorporates the changes listed in the abovementioned errata.
Recent publications:
Preprints of most of my recent papers (in pdf format) may be obtained by clicking on the paper titles below.
- (with C. Semple and G. Whittle) An upgraded Wheels-and-Whirls Theorem for 3-connected matroids, submitted.
- (with C. Semple and G. Whittle) Exposing 3-separations in 3-connected matroids, submitted.
- (with N. Hine) When excluding one matroid prevents infinite antichains, Adv. in Appl. Math., to appear.
- (with C. Chun) Unavoidable parallel minors of regular matroids, European J. Combin., to appear.
- (with D. Mayhew, B. Oporowski, and G. Whittle) The excluded minors for the matroids that are binary or ternary, submitted.
- (with C. Chun and D. Mayhew) A chain theorem for internally 4-connected binary matroids, submitted.
- (with J. Aikin) The structure of crossing separations in matroids, Adv. in Appl. Math.41 (2008), 10-26.
- (with C. Semple and G. Whittle) Maintaining 3-connectivity relative to a fixed basis, Adv. in Appl. Math. 41 (2008), 1-9.
- (with B. Beavers) Constructive characterizations of 3-connected matroids of path width three, Europ. J. Combin., 29 (2008), 1643-1661.
- (with C. Semple and G. Whittle) A chain theorem for matroids, J. Combin. Theory Ser. B 98 (2008), 447-483.
- (with C. Semple and G. Whittle) Wild triangles in 3-connected matroids, J. Combin. Theory Ser. B 98 (2008), 291-323.
- (with C. Semple and G. Whittle) The structure of the 3-separations of 3-connected matroids II, Europ. J. Combin. 28 (2007), 1239-1261.
- (with R. Hall and C. Semple), The structure of 3-connected matroids of path width three, Europ. J. Combin. 28 (2007), 964-989.
- The contributions of Dominic Welsh to matroid theory, in Combinatorics, Complexity, and Chance (G. Grimmett and C. McDiarmid eds.), Oxford Univ. Press, Oxford, 2007, pp.234-259.
- (with M. Lemos), Matroid covering and packing with circuits through an element, J. Combin. Theory Ser. B 96 (2006), 135-158.
- (with B. Beavers) On pancyclic representable matroids, Discrete Math. 305 (2005), 337-343.
- (with R. Hall and C. Semple), The structure of equivalent 3-separations in a 3-connected matroid, Adv. in Appl. Math. 35 (2005), 123-181.
- (with H. Wu), The 3-connected graphs with exactly three non-essential edges, Graphs Combin. 20 (2004), 233-246.
- (with C. Semple and G. Whittle) The structure of the 3-separations of 3-connected matroids, J. Combin. Theory Ser. B 92 (2004), 257-293.
- (with J.F. Geelen, D.L. Vertigan, and G.P. Whittle), A short proof of non-GF(5)-representability of matroids, J. Combin. Theory Ser. B 91 (2004), 105-121.
- (with R. Hall, C. Semple, and G. Whittle), Fork-decompositions of matroids, Adv. in Appl. Math. 32 (2004), 523-575.
- (with M. Lemos), On the minor-minimal 2-connected graphs having a fixed minor, Discrete Math. 280 (2004), 77-118.
- (with A.M. Hobbs), William T. Tutte, 1917-2002, Notices Amer. Math. Soc. 51 (2004), 320-330.
- (with Y.-B. Choe, A.D. Sokal, and D.G. Wagner), Homogeneous multivariate polynomials with the half-plane property, Adv. in Appl. Math. 32 (2004), 88-187.
- (with M. Lemos), On the minor-minimal 3-connected matroids having a fixed minor, Europ. J. Combin. 24 (2003), 1097-1123.
- (with B. Chaourar) On series-parallel extensions of uniform matroids, Europ. J. Combin. 24 (2003), 877-879.
- The structure of a 3-connected matroid with a 3-separating set of essential elements, Discrete Math. 265 (2003), 173-187.
- (with M. Lemos), On removable cycles through every edge, J. Graph Theory 42 (2003), 155-164.
- (with R. Hall, C. Semple, and G. Whittle), On matroids of branch-width three, J. Combin. Theory Ser. B 86 (2002), 148-171.
- (with D. Welsh), Chromatic, flow, and reliability polynomials: the complexity of their coefficients, Combinatorics, Probability and Computing 11 (2002), 403-426.
- (with J.F. Geelen, D.L. Vertigan, and G.P. Whittle), Totally free expansions of matroids, J. Combin. Theory Ser. B 84 (2002), 130-179.
- (with C. Semple, D. Vertigan, and G. Whittle), Infinite antichains of matroids with characteristic set p, Discrete Math. 242 (2002), 175-185.
- On the interplay between graphs and matroids, Surveys in Combinatorics, 2001 (Sussex) (J.W.P. Hirschfeld ed.) London Math. Soc. Lecture Notes 288 , Cambridge Univ. Press, Cambridge, 2001, pp. 199-239.
- (with M. Lemos), A sharp bound on the size of a connected matroid, Trans. Amer. Math. Soc. 353(2001), 4039-4056.
- (with J.F. Geelen, D.L. Vertigan, and G.P. Whittle), On the excluded minors for quaternary matroids, J. Combin. Theory Ser. B 80 (2000), 57-68.
- with H. Wu), On the structure of 3-connected matroids and graphs, Europ. J. Combin. 21 (2000), 667-688.
- (with M. Lemos and T.J. Reid), On the 3-connected matroids that are minimal having a fixed restriction, Graphs and Combin. 16 (2000), 285-318.
- (with C. Semple and D. Vertigan), Generalized Delta - Y exchanges and k-regular matroids, J. Combin. Theory Ser. B 79 (2000), 1-65.
- with M. Lemos), On size, circumference and circuit removal in 3-connected matroids, Discrete Math. 220 (2000), 145-157.
- (with H. Wu), Matroids and graphs with few non-essential elements, Graphs and Combin. 16 (2000), 199-229.
- (with G. Whittle), On the non-uniqueness of q-cones of matroids, Discrete Math. 218 (2000), 271-275.
- (with M. Lemos), On the 3-connected matroids that are minimal having a fixed spanning restriction, Discrete Math. 218 (2000), 131-165.
- (with G. Ding, B. Oporowski, and D. Vertigan), Unavoidable minors of large 3-connected matroids, J. Combin. Theory Ser. B 71 (1997), 244-293.
- (with D. Vertigan and G. Whittle), On inequivalent representations of matroids over finite fields, J. Combin. Theory Ser. B 67 (1996), 325-343.
- (with G. Ding, B. Oporowski, and D. Vertigan), Unavoidable minors of large 3-connected binary matroids, J. Combin. Theory Ser. B 66 (1996), 334-360.
- Structure theory and connectivity for matroids, Matroid Theory (J. Bonin, J. Oxley, and B. Servatius eds.) Contemporary Mathematics 197 (Amer. Math. Soc., Providence), (1996), pp. 129-170.
- (with B. Oporowski and R. Thomas), Typical subgraphs of 3- and 4-connected graphs, J. Combin. Theory Ser. B 57 (1993), 239-257.
- (with S. Akkari) Some local extremal connectivity results for matroids, Combinatorics, Probability and Computing 2 (1993), 367-384.
- (with T. Brylawski) The Tutte polynomial and its applications, in Matroid Applications (N. White ed.), Cambridge Univ. Press, Cambridge, 1992, pp.123-225.
- A characterization of a class of non-binary matroids, J. Combin. Theory Ser. B 49 (1990), 181-189.
- The binary matroids with no 4-wheel minor, Trans. Amer. Math. Soc. 301 (1987), 63-75.
- On non-binary 3-connected matroids, Trans. Amer. Math. Soc. 300 (1987), 663-679.
- A characterization of the ternary matroids with no M(K_4)-minor, J. Combin. Theory Ser. B 42 (1987), 212-249.
- On the intersections of circuits and cocircuits in matroids, Combinatorica 4 (1984), 187-195.
- On a matroid generalization of graph connectivity, Math. Proc. Camb. Phil. Soc.90 (1981), 207-214.
- On matroid connectivity, Quart. J. Math. Oxford Ser. 2 32 (1981), 193-208.
Office Location and Phone: 370 Lockett Hall. (225) 578 1577
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