Arthur Marmaduke Hobbs (19 June 1940 – 25 October 2020)[1] was an American mathematician specializing in graph theory.
The family moved in 1941 to Pennsylvania, and again after World War II to South Bend, Indiana, where Arthur Hobbs grew up.
He then served in the US Army in Washington, D.C., for approximately two years, and then from 1965 to 1968 worked for the National Bureau of Standards.
After receiving his Ph.D., Hobbs began teaching as a mathematics professor at Texas A&M University in 1971, where he worked until his retirement in 2008.
Later, in graduate school and for ten years following, he concentrated on Hamiltonian cycles, particularly in squares and higher powers of graphs.
They defined the fractional arboricity of a graph as where ω(H is the number of components of H and the maximum is taken over all subgraphs H for which the denominator is not zero.