|Died||20 January 2001(aged 68)|
|Alma mater||University of Cambridge|
|Institutions||University of Waterloo|
|Doctoral advisor||Shaun Wylie|
|Doctoral students||Václav Chvátal|
Nash-Williams was born on 19 December 1932 in Cardiff, Wales; his father, Victor Erle Nash-Williams, was an archaeologist at University College Cardiff, and his mother had studied classics at Oxford University. After studying mathematics at Cambridge University, earning the title of Senior Wrangler in 1953, he remained for his graduate studies at Cambridge, studying under the supervision of Shaun Wylie and David Rees. He continued his studies for a year at Princeton University, with Norman Steenrod; all three of Wylie, Rees, and Steenrod are listed as the supervisors of his Ph.D. dissertation. He finished his dissertation in 1958, but before doing so he returned to the UK as an assistant lecturer at the University of Aberdeen. He kept his position at Aberdeen through ten years and two promotions until 1967, when he moved to the University of Waterloo and became one of the three faculty members in the newly formed Department of Combinatorics there. In 1972 he returned to Aberdeen, as Professor of Pure Mathematics; in 1975 he moved to the University of Reading, where he took the chair previously held by Richard Rado, who had been one of his dissertation examiners. In 1996 he retired; he died on 20 January 2001 in Ascot, Berkshire, where his brother was rector.
Awards and honours
He was elected to the Royal Society of Edinburgh in 1969. In 1994, the University of Waterloo gave him an honorary doctorate for his contributions to combinatorics. A conference in his honor was held on his retirement in 1996, the proceedings of which were published as a festschrift. The 18th British Combinatorial Conference, held in Sussex in July 2001, was dedicated to his memory.
Hilton writes that "Themes running through his papers are Hamiltonian cycles, Eulerian graphs, spanning trees, the marriage problem, detachments, reconstruction, and infinite graphs." In his first papers Nash-Williams considered the knight's tour and random walk problems on infinite graphs; the latter paper included an important recurrence criterion for general Markov chains, and was also the first to apply electrical network techniques of Rayleigh to random walks. His dissertation, which he finished in 1958, concerned generalizations of Euler tours to infinite graphs. Welsh writes that his subsequent work defining and characterizing the arboricity of graphs (discovered in parallel and independently by W. T. Tutte) has "had a huge impact," in part because of its implications in matroid theory. Nash-Williams also studied k-edge-connected graphs, Hamiltonian cycles in dense graphs, versions of the reconstruction conjecture for infinite graphs, and the theory of quasi-orders. He also gave a short elegant proof of Kruskal's tree theorem.
- Nash-Williams biography from the MacTutor history of mathematics archive.
- Welsh, D. J. A. (2003), "Obituary: Crispin St J. A. Nash-Williams (1932-2001)", Bull. London Math. Soc., 35 (6): 829–844, doi:10.1112/S0024609303002315.
- Hilton, A. J. W. (2001), "Crispin St J A Nash-Williams", Bull. Inst. Combin. Appl., 33: 11–12.