Crispin St John Alvah Nash-WilliamsFRSE (19 December 1932 – 20 January 2001) was a British mathematician. His research interest was in the field ofdiscrete mathematics, especiallygraph theory.

Nash-Williams was born on 19 December 1932 inCardiff, Wales. His father,Victor Erle Nash-Williams (né Williams), was an archaeologist atUniversity College Cardiff, and his mother had studied classics atOxford. As a small boy, Nash-Williams attendedChrist Church Cathedral School inOxford, which was then headed byWilfrid Oldaker. A biographer has said that Oldaker was a formative influence on Nash-Williams.^[1] He then attendedRugby School until the age of 18.^[1]

After studying mathematics as an undergraduate atTrinity Hall, Cambridge, earning the title ofSenior Wrangler in 1953, he remained there for his graduate studies, under the supervision ofShaun Wylie andDavid Rees. He then continued his education for a year atPrinceton University, withNorman 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 Britain as an assistant lecturer at theUniversity of Aberdeen.

He remained in Aberdeen for ten years, during which time he was twice promoted. In 1967 he moved to theUniversity of Waterloo and became one of the three faculty members in the newly formed Department of Combinatorics and Optimization there. In 1972, he returned to Aberdeen as Professor of Pure Mathematics, but stayed only briefly, moving to theUniversity of Reading in 1975. There he succeededRichard Rado, who had earlier been one of his dissertation examiners.

He retired in 1996 and died on 20 January 2001, aged 68, inAscot, Berkshire, where his brother was rector.^[2][1]

He was elected to theRoyal Society of Edinburgh in 1969. In 1994, the University of Waterloo gave him an honorary doctorate for his contributions tocombinatorics. A conference in his honor was held on his retirement in 1996, the proceedings of which were published as afestschrift. The 18th British Combinatorial Conference, held in Sussex in July 2001, was dedicated to his memory.^[1]

He is known for theNash-Williams theorem.

Hilton^[3] writes that "Themes running through his papers areHamiltonian cycles,Eulerian graphs,spanning trees, themarriage problem, detachments,reconstruction, and infinite graphs."In his first papers Nash-Williams considered theknight's tour andrandom walk problems on infinite graphs; the latter paper included an important recurrence criterion for generalMarkov chains, and was also the first to apply electrical network techniques ofRayleigh to random walks. His dissertation, which he finished in 1958, concerned generalizations ofEuler tours to infinite graphs.^[2][1]

Welsh writes that his subsequent work defining and characterizing thearboricity of graphs (discovered in parallel and independently byW. T. Tutte) has "had a huge impact," in part because of its implications inmatroid theory. Nash-Williams also studiedk-edge-connected graphs, Hamiltonian cycles indense graphs, versions of thereconstruction conjecture for infinite graphs, and the theory ofquasi-orders. He also gave a short elegant proof ofKruskal's tree theorem.^[1]

• List of University of Waterloo people

• Crispin Nash-Williams at theMathematics Genealogy Project