User:Qcmath14/sandbox

Early life

Arthur Hobbs was born on June 6, 1940 in Washington D.C. He is the eldest child of his family, having two younger brothers. His mother, who is now 95 years of age, was a stay at home mother, while his father was an engineer, and later became an attorney. In 1941, Arthur Hobbs and his family moved to Pennsylvania. Later, after WWII had ended in 1945, his family moved again to South Bend, Indiana, which is where Arthur Hobbs grew up. In 1964, Arthur Hobbs married his wife Barbara. Currently, Arthur Hobbs and his wife have two daughters, Melissa and Patricia, and have five grandchildren.

Education

a)High School: Arthur Hobbs attended John Adams High School located in South Bend, Indiana. He recalls having a mathematics teacher named Mr. Weir whom he considered to be a particularly good teacher. Arthur Hobbs graduated high school in 1958, with a partial tuition and partial housing scholarship.

b)Undergraduate: Arthur Hobbs attending the University of Michigan. He studied mathematics, and graduated in 1962. Upon graduating, Arthur Hobbs joined the army in 1963, in which he served in Washington D.C for about two years. He then worked for the National Bureau of Standards in Washington D.C from 1965-1968.

c) Doctorate: In 1968, Arthur Hobbs wrote a letter to the University of Waterloo located in Ontario, Canada. In his letter, he explained his interest in mathematics and his desire to study Graph Theory. Arthur Hobbs’ admission was accepted, and additionally, he received a partial scholarship towards his tuition. His research focused on Hamiltonian Cycles,particularly concentrating in squares and higher powers of graphs,and his thesis adviser was the well-known Graph Theorist, William Thomas Tutte. Arthur Hobbs completed his study and received his Ph.D in 1971.

Career

After receiving his Ph.D, Dr.Hobbs began teaching as a mathematics professor at Texas A&M University in 1971, where he worked until his retirement in 2008. He was the faculty senator for twelve years, and also taught various mathematics courses including, but not limited to calculus, combinatorics, finite mathematics, graph theory, and number theory. Dr. Hobbs and his colleague taught a course in the intersection of graph theory and number theory, he explains:

We taught enough of the elements of our specialties that students could read a research paper including elements of both subjects. Then students were asked to select a paper from a list we provided, read it, and report on it to the class. An important aspect of the course was gaining a feeling for the discovery process involved in research. We asked about each idea presented, "Are there questions that are not addressed here? Can these ideas be extended in ways the authors did not discuss?" There was a test on each of number theory and graph theory just after the lectures on that topic, and the grade was based on the results of those tests and on the presentations made. One consequence of this course was a published research paper

Research in Mathematics and Contributions

Graph Theory: Dr. Arthur Hobbs' research before entering graduate school was on thickness of graphs. Later, in graduate school and for ten years following he concentrated on Hamiltonian cycles, particularly in squares and higher powers of graphs. He then spent a couple of years working on the Gyarfas and Lehel conjecture that any family of trees T1; T2; : : : Tn, with 1; 2; : : : ; n vertices respectively, can be packed in an edge-disjoint manner into the complete graph on n vertices. This conjecture is still open. Dr. Arthur Hobbs has also worked with packings of graphs with trees and coverings by trees, which he worked on with several co-authors, including Paul A. Catlin, Jerrold W. Grossman, Lavanya Kannan, and Hong-Jian Lai.

They defined the fractional arboricity of a graph as $$\gamma(G) = max_{H \subseteq G}({|E(H)}|\over{|V(H)| - \omega(H)}),$$ where $\omega(H)$ is the number of components of H and the maximum is taken over all subgraphs H for which the denominator is not zero. They also defined the strength of a graph as $$\eta(G) = min_{S \subseteq E(G)}({|S|}\over{\omega(G-S)-\omega(G)}),$$ where the maximum is taken over all subsets S of E(G) for which the denominator is not zero. Additionally, they characterized uniformly dense graphs, and have found several classes of uniformly dense graphs and several ways of constructing such graphs. Furthermore, Dr. Hobbs has done research in Matroid Theory.

http://www.math.tamu.edu/~arthur.hobbs/

Publications

Dr. Hobbs has 40 publications regarding his work in graph theory. Additionally, in 1989 he co-authored a book on linear algebra titled, Elementary Linear Algebra. He has also written an essay on how to read research papers. A few publications are listed below:

1) Hobbs, Arthur M.; Kannan, Lavanya; Lai, Hong-Jian; Lai, Hongyuan; Weng, Guoqing Balanced and 1-balanced graph constructions. Discrete Appl. Math. 158 (2010), no. 14, 1511–1523.

2) Fleischner, Herbert; Hobbs, Arthur M.; Tapfuma Muzheve, Michael Hamiltonicity in vertex envelopes of plane cubic graphs. Discrete Math. 309 (2009), no. 14, 4793–4809.

3) Kannan, Lavanya; Hobbs, Arthur; Lai, Hong-Jian; Lai, Hongyuan Transforming a graph into a 1-balanced graph. Discrete Appl. Math. 157 (2009), no. 2, 300–308

4) A. M. Hobbs, H.-J. Lai, H. Lai, and G. Weng, Constructing Uniformly Dense Graphs, preprint, October 1, 1994

Personal Interests and Hobbies

In addition to being a graph theorist with interests in Hamiltonian cycles, packings and coverings by trees, and matroid theory relating to packings and coverings, Dr. Hobbs is fond of contra, round dancing, and square dancing, and has taught round dance as a hobby. He also enjoys collecting books, paintings, and stamps. Additonally,he has a substantial interest in history; predominantly in the history of mathematics. Furthermore, he greatly cares about space flight, and views it as essential for the future of mankind.

Resources

- I have used Dr. Arthur Hobbs himself as one of my resources

- http://www.math.tamu.edu/~arthur.hobbs/

- http://www.ams.org/mathscinet/search/publications.html?pg1=INDI&s1=86630