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Dominic Welsh (1938-2023)

Published 22 Apr 2024 in math.HO and math.CO | (2404.13942v1)

Abstract: This biographical and scientific memoir of Dominic Welsh includes summaries of his important contributions to probability and combinatorics. With John Hammersley, he introduced first-passage percolation, and in so doing they formulated and proved the first subadditive ergodic theorem. Welsh has numerous results in matroid theory, and wrote the first monograph on the topic. He worked on computational complexity and particularly the complexity of computing the Tutte polynomial. He was an inspirational teacher and advisor who helped to develop a community of scholars in combinatorics.

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References (122)
  1. Publications of Dominic Welsh, https://www.statslab.cam.ac.uk/~grg/papers/welsh-bib.pdf.
  2. Swansea professor’s maths victory, https://www.walesonline.co.uk/news/wales-news/swansea-professors-maths-victory-2122483.
  3. 1962
  4. Further results on the rate of convergence to the connective constant of the hypercubical lattice. Quart. J. Math. Oxford Ser. (2), 13:108–110, 1962. 1964
  5. D. J. A. Welsh. Topics in Stochastic Processes with special reference to First Passage Percolation Theory. D.Phil. Thesis, University of Oxford, 1964, 131 pp. 1965
  6. First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. In Bernoulli, Bayes, Laplace Anniversary Volume, pages 61–110. Springer, New York, 1965.
  7. A two-dimensional Poisson growth process. J. Roy. Statist. Soc. Ser. B, 27:497–504, 1965.
  8. D. J. A. Welsh. Letter to the Editor: Errors introduced by a PERT assumption. Operat. Res., 13:141–143, 1965. 1966
  9. D. J. A. Welsh. Letter to the Editor: Super-critical arcs of a PERT network. Operat. Res. 14:173–174, 1966.
  10. A note on the monomer dimer problem. Proc. Cambridge Philos. Soc., 62:503–505, 1966. 1967
  11. D. J. A. Welsh. On dependence in matroids. Canad. Math. Bull., 10:599–603, 1967.
  12. An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer J., 10:85–86, 1967. 1968
  13. D. J. A. Welsh. Some applications of a theorem of Rado. Mathematika, 15:199–203, 1968.
  14. D. J. A. Welsh. Kruskal’s theorem for matroids. Proc. Cambridge Philos. Soc., 64:3–4, 1968. 1969
  15. Matroids versus graphs. In The Many Facets of Graph Theory (Proc. Conf., Western Mich. Univ., Kalamazoo, Mich., 1968), Lecture Notes in Math., volume 110, pages 155–170. Springer, New York, 1969.
  16. D. J. A. Welsh. Transversal theory and matroids. Canadian J. Math., 21:1323–1330, 1969.
  17. D.  J. A. Welsh. A bound for the number of matroids. J. Combin. Theory, 6:313–316, 1969.
  18. D. J. A. Welsh. Euler and bipartite matroids. J. Combin. Theory, 6:375–377, 1969.
  19. D. J. A. Welsh. On the hyperplanes of a matroid. Proc. Cambridge Philos. Soc., 65:11–18, 1969. 1970
  20. On removing a point of a digraph. Studia Sci. Math. Hungar., 5:299–301, 1970.
  21. D. J. A. Welsh. Probability theory and its applications. In Mathematics Applied to Physics, pages 465–561. Springer, New York, 1970.
  22. D. J. A. Welsh. On matroid theorems of Edmonds and Rado. J. London Math. Soc. (2), 2:251–256, 1970.
  23. On the vector representation of matroids. J. London Math. Soc. (2), 2:284–288, 1970. 1971
  24. D. J. A. Welsh. Matroids and block designs. In Théorie des Matroïdes (Rencontre Franco-Britannique, Brest, 1970), Lecture Notes in Math., volume 211, pages 95–106. Springer, Berlin, 1971.
  25. D. J. A. Welsh. Related classes of set functions. In Studies in Pure Mathematics (Presented to Richard Rado), pages 261–269. Academic Press, London, 1971.
  26. Some results on transversal matroids and constructions for identically self-dual matroids. Quart. J. Math. Oxford Ser. (2), 22:435–451, 1971.
  27. D. J. A. Welsh. Generalized versions of Hall’s theorem. J. Combin. Theory Ser. B, 10:95–101, 1971.
  28. The number of combinatorial geometries. Bull. London Math. Soc., 3:55–56, 1971.
  29. D. J. A. Welsh (ed.). Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969). Academic Press, London, 1971.
  30. D. J. A. Welsh. Combinatorial problems in matroid theory. In Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), pages 291–306. Academic Press, London, 1971. 1972
  31. Supermatroids. In Combinatorics (Proc. Conf., Oxford, 1972), pages 72–122. Inst. Math. Appl., Southend-on-Sea, 1972.
  32. J. de Sousa and D. J. A. Welsh. A characterisation of binary transversal structures. J. Math. Anal. Appl., 40:55–59, 1972.
  33. On the automorphism group of a matroid. Discrete Math., 2:163–171, 1972.
  34. D. J. A. Welsh and D. R. Woodall (eds.). Combinatorics (Proc. Conf., Oxford, 1972). Institute of Mathematics and its Applications, Southend-on-Sea, 1972. 1973
  35. A greedy algorithm for solving a certain class of linear programmes. Math. Programming, 5:338–353, 1973. 1975
  36. A note on matroids and block designs. J. Austral. Math. Soc., 20:54–58, 1975.
  37. Combinatorial applications of an inequality from statistical mechanics. Math. Proc. Cambridge Philos. Soc., 77:485–495, 1975. 1976
  38. On the computational complexity of graph theoretical properties. In Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975), Congress. Numer., volume XV, pages 471–487, 1976.
  39. D. J. A. Welsh. Matroid Theory. Lond. Math. Soc. Monographs, volume 8, Academic Press, London, 1976. 1978
  40. Percolation probabilities on the square lattice. Ann. Discrete Math., 3:227–245, 1978. 1979
  41. D. J. A. Welsh. Colouring problems and matroids. In Surveys in Combinatorics (Proc. Seventh British Combinatorial Conf., Cambridge, 1979), London Math. Soc. Lecture Note Ser., volume 38, pages 229–257. Cambridge Univ. Press, Cambridge, 1979.
  42. On some percolation results of J. M. Hammersley. J. Appl. Probab., 16:526–540, 1979.
  43. The Tutte polynomial and percolation. In Graph Theory and Related Topics (Proc. Conf., Univ. Waterloo, Waterloo, Ont., 1977), pages 329–339. Academic Press, New York-London, 1979. 1980
  44. D. J. A. Welsh. Colourings, flows and projective geometry. Nieuw Arch. Wisk. (3), 28:159–176, 1980.
  45. On the chromatic number of binary matroids. Mathematika, 27:1–9, 1980.
  46. The computational complexity of matroid properties. Math. Proc. Cambridge Philos. Soc., 87:29–45, 1980. 1981
  47. Animals, trees and renewal sequences. IMA J. Appl. Math., 27:1–17, 1981. 1982
  48. D. J. A. Welsh. Matroids and combinatorial optimisation. In Matroid Theory and its Applications, pages 323–416. Liguori, Naples, 1982.
  49. D. J. A. Welsh. Problems in computational complexity. Shiva Math. Ser., 6:75–85, 1982.
  50. Tangential 1111-blocks over GF⁢(3)GF3{\rm GF}(3)roman_GF ( 3 ). Discrete Math., 40:319–320, 1982.
  51. Some colouring problems and their complexity. Ann. Discrete Math., 13:159–170, 1982.
  52. Flow in networks with random capacities. Stochastics, 7:205–229, 1982.
  53. Corrigendum: “Animals, trees and renewal sequences” [IMA J. Appl. Math. 27:1–17, 1981]. IMA J. Appl. Math., 28:107, 1982. 1983
  54. Finite particle systems and infection models. Math. Proc. Cambridge Philos. Soc., 94:167–182, 1983.
  55. D. J. A. Welsh. Randomised algorithms. Discrete Appl. Math., 5:133–145, 1983. 1984
  56. The antivoter problem: random 2222-colourings of graphs. In Graph Theory and Combinatorics (Cambridge, 1983), pages 133–144. Academic Press, London, 1984. 1986
  57. D. J. A. Welsh. Correlated percolation and repulsive particle systems. In Stochastic Spatial Processes (Heidelberg, 1984), Lecture Notes in Math., volume 1212, pages 300–311. Springer, Berlin, 1986.
  58. Probability, an Introduction. Clarendon Press, Oxford, 1986. 1988
  59. D. J. A. Welsh. Matroids and their applications. In Selected Topics in Graph Theory, 3, pages 43–70. Academic Press, San Diego, CA, 1988.
  60. D. J. A. Welsh. Codes and Cryptography. Clarendon Press, Oxford, 1988. 1989
  61. A randomised 3333-colouring algorithm. Discrete Math., 74: 253–261, 1989. 1990
  62. G. R. Grimmett and D. J. A. Welsh (eds.). Disorder in Physical Systems, A Volume in Honour of J.  M. Hammersley. Clarendon Press, Oxford, 1990.
  63. D. J. A. Welsh. The computational complexity of some classical problems from statistical physics. In Disorder in Physical Systems, A Volume in Honour of J.  M. Hammersley, pages 307–321. Clarendon Press, Oxford, 1990.
  64. On the computational complexity of the Jones and Tutte polynomials. Math. Proc. Cambridge Philos. Soc., 108:35–53, 1990. 1991
  65. D. J. A. Welsh. Colouring and knot polynomials. In Recent Developments and Applications in Mathematics and Computer Science (Trieste, 1990), pages 112–131. World Sci. Publ., River Edge, NJ, 1991. 1992
  66. D. J. A. Welsh. On the number of knots and links. In Sets, Graphs and Numbers (Budapest, 1991), Colloq. Math. Soc. János Bolyai, volume 60, pages 713–718. North-Holland, Amsterdam, 1992.
  67. Tutte polynomials computable in polynomial time. Discrete Math., 109:185–192, 1992.
  68. The computational complexity of the Tutte plane: the bipartite case. Combin. Probab. Comput., 1:181–187, 1992. 1993
  69. D. J. A. Welsh. Complexity: Knots, Colourings and Counting. London Math. Soc. Lecture Note Series, volume 186. Cambridge Univ. Press, Cambridge, 1993.
  70. D. J. A. Welsh. Percolation in the random cluster process and Q𝑄Qitalic_Q-state Potts model. J. Phys. A, 26:2471–2483, 1993.
  71. D. J. A. Welsh. Knots and braids: some algorithmic questions. In Graph Structure Theory (Seattle, WA, 1991), Contemp. Math., volume 147, pages 109–123. Amer. Math. Soc., Providence, RI, 1993.
  72. D. J. A. Welsh. The complexity of knots. Ann. Discrete Math., 55:159–171, 1993.
  73. Knots, matroids and the Ising model. Math. Proc. Cambridge Philos. Soc., 113:107–139, 1993. 1994
  74. D. J. A. Welsh. The computational complexity of knot and matroid polynomials. Discrete Math., 124:251–269, 1994.
  75. Polynomial time randomised approximation schemes for the Tutte polynomial of dense graphs. In 35th Annual Symposium on Foundations of Computer Science (Santa Fe, NM, 1994), pages 24–35. IEEE Comput. Soc. Press, Los Alamitos, CA, 1994.
  76. D. J. A. Welsh. Random generation of polymer configurations. In Probability, Statistics and Optimisation, pages 65–77. Wiley, Chichester, 1994.
  77. D. J. A. Welsh. The random cluster process. Discrete Math., 136:373–390. 1994.
  78. D. J. A. Welsh. Randomised approximation in the Tutte plane. Combin. Probab. Comput., 3:137–143, 1994. 1995
  79. D. J. A. Welsh. Randomised approximation schemes for Tutte-Gröthendieck invariants. In Discrete Probability and Algorithms (Minneapolis, MN, 1993), IMA Vol. Math. Appl., volume 72, pages 133–148. Springer, New York, 1995.
  80. Combinatorics in pure mathematics. In Handbook of Combinatorics, Vol. 1, 2, pages 2039–2082. Elsevier, Amsterdam, 1995.
  81. Combinatorics in statistical physics. In Handbook of Combinatorics, Vol. 1, 2, pages 1925–1954. Elsevier, Amsterdam, 1995.
  82. D. J. A. Welsh. Matroids: fundamental concepts. In Handbook of Combinatorics, Vol. 1, 2, pages 481–526. Elsevier, Amsterdam, 1995.
  83. Polynomial time randomized approximation schemes for Tutte-Gröthendieck invariants: the dense case. Random Structures Algorithms, 6:459–478, 1995.
  84. The Markov chain of colourings. In Integer Programming and Combinatorial Optimization (Copenhagen, 1995), Lecture Notes in Comput. Sci., volume 920, pages 373–387. Springer, Berlin, 1995. 1996
  85. Randomised approximation of the number of bases. In Matroid Theory (Seattle, WA, 1995), Contemp. Math., volume 197, pages 371–376. Amer. Math. Soc., Providence, RI, 1996.
  86. D. J. A. Welsh. Counting colourings and flows in random graphs. In Combinatorics, Paul Erdős is Eighty, Vol. 2 (Keszthely, 1993), Bolyai Soc. Math. Stud., volume 2, pages 491–505. János Bolyai Math. Soc., Budapest, 1996.
  87. The random planar graph. Congr. Math., 113:61–79. 1996 (Festschrift for C. St. J. A. Nash-Williams). 1997
  88. D. J. A. Welsh. Knots. In Graph Connections, Oxford Lecture Ser. Math. Appl., volume 5, pages 176–193. Oxford Univ. Press, Oxford, 1997.
  89. D. J. A. Welsh. Approximate counting. In Surveys in Combinatorics, 1997 (London), London Math. Soc. Lecture Note Ser., volume 241, pages 287–323. Cambridge Univ. Press, Cambridge, 1997.
  90. D. J. A. Welsh. Randomised approximation in the Tutte plane. In Combinatorics, Geometry and Probability (Cambridge, 1993), pages 549–555. Cambridge Univ. Press, Cambridge, 1997.
  91. The polytope of win vectors. Ann. Comb., 1:1–15, 1997.
  92. Lê numbers of arrangements and matroid identities. J. Combin. Theory Ser. B, 70:118–133, 1997. 1998
  93. D. J. A. Welsh. Percolation and the random cluster model: combinatorial and algorithmic problems. Algorithms Combin., 16:166–194, 1998. 1999
  94. C. Merino and D. J. A. Welsh. Forests, colorings and acyclic orientations of the square lattice. Ann. Comb., 3:417–429. 1999.
  95. Arrangements, channel assignments, and associated polynomials. Adv. in Appl. Math., 23:375–406, 1999.
  96. D. J. A. Welsh. The Tutte polynomial. Random Struct. Alg., 15:210–228. 1999.
  97. A weighted graph polynomial from chromatic invariants of knots. Ann. Inst. Fourier (Grenoble), 49:1057–1087. 1999. 2000
  98. D. J. A. Welsh and C. Merino. The Potts model and the Tutte polynomial. J. Math. Phys., 41:1127–1152. 2000.
  99. Knot graphs. J. Graph Theory, 34:100–111, 2000. 2001
  100. The complexity of counting problems. In Aspects of Complexity (Kaikoura, 2000), De Gruyter Ser. Log. Appl., volume 4, pages 115–153. De Gruyter, Berlin, 2001. 2002
  101. Chromatic, flow and reliability polynomials: the complexity of their coefficients. Combin. Probab. Comput., 11:403–426, 2002.
  102. On the parity of colourings and flows. J. Combin. Theory Ser. B, 84:364–365, 2002. 2003
  103. D. J. A. Welsh. Crispin St. J. A. Nash-Williams (1932–2001). Bull. London Math. Soc., 35:829–844, 2003. 2004
  104. A linking polynomial of two matroids. Adv. in Appl. Math., 32:391–419. 2004.
  105. D. J. A. Welsh. W. T. (Bill) Tutte—in memoriam. Adv. in Appl. Math., 32:3–4. 2004. 2005
  106. Approximate counting and quantum computation. Combin. Probab. Comput., 14:737–754, 2005.
  107. Random planar graphs. J. Combin. Theory Ser. B, 93:187–205, 2005. 2006
  108. Random graphs from planar and other addable classes. Algorithms Combin., 26:231–246, 2006.
  109. Complexity and Cryptography. Cambridge Univ. Press, Cambridge, 2006. 2007
  110. John Michael Hammersley, 21 March 1920–2 May 2004. Biogr. Mems Fell. R. Soc., 53:163–183, 2007. Reprinted in Bull. London Math. Soc., 41(6):1125–1143, 2009. 2008
  111. Negative correlation in graphs and matroids. Combin. Probab. Comput., 17:423–435, 2008. 2009
  112. D. J. A. Welsh. Some problems on approximate counting in graphs and matroids. In Research Trends in Combinatorial Optimization, pages 523–544. Springer, Berlin, 2009. 2010
  113. D. J. A. Welsh. Matroids and combinatorial optimisation. In Matroid Theory and its Applications, C.I.M.E. Summer Sch., volume 83, pages 323–416. Springer, Heidelberg, 2010.
  114. Growth constants of minor-closed classes of graphs. J. Combin. Theory Ser. B, 100:468–484, 2010. 2011
  115. On the asymptotic proportion of connected matroids. European J. Combin., 32:882–890, 2011.
  116. Optimizing phylogenetic diversity with ecological constraints. Ann. Comb., 15:255–266, 2011. 2012
  117. Corrigendum to “A linking polynomial of two matroids” [Adv. in Appl. Math. 32:391–419, 2004]. Adv. in Appl. Math., 49:78–79, 2012. 2013
  118. On the number of sparse paving matroids. Adv. in Appl. Math., 50:125–131, 2013.
  119. On properties of almost all matroids. Adv. in Appl. Math., 50:115–124, 2013. 2014
  120. Probability, an Introduction. Oxford Univ. Press, Oxford, 2nd edition, 2014. 2015
  121. Counting phylogenetic networks. Ann. Comb., 19:205–224, 2015.
  122. Special issue in honour of James Oxley. Ann. Comb., 19:1–5, 2015.
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  1. Geoffrey R. Grimmett 

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