You are visitor number to this page since the counter was set up on August 12, 1996. This counter is provided courtesy of WEB Counter .## Photo shows me in PhD robes of the University of Waterloo

My office is Room 218 in Milner Hall.

My mailing address is:

Prof. Arthur M. Hobbs AMS Classification 05C Department of Mathematics Also interested in 05B35, 01-XX Texas A&M University College Station, TX 77843

Office phone: (979)-845-3250

Home phone: (979)-846-9376

e-mail: hobbs@math.tamu.edu

Here are my wife, Barbara, and myself at a new years party:

I have been very fortunate in the many friends I have had. The following photograph shows me between two of them. The one on my left is my thesis advisor, the outstanding graph and matroid theorist, William T. Tutte. The one on my right was one of the most prolific mathematicians who ever lived and was the founder of several branches of mathematics, Paul Erdos. (There should be a Hungarian umlaut above the o of Erdos's name, but I don't know how to produce one in html.) So here we are, from left to right, Paul Erdos, Arthur Hobbs, and William T. Tutte. The picture was taken at Western Michigan University at the Quadrennial conference on May 7, 1980, by my mother, Helen Hobbs.

TAMU Faculty Facts: Answers to Questions About Faculty Roles and Responsibilities at Texas A&M University

This document is now out of date. I hope another faculty member will someday update it and get it published again.

- 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, I collect books, paintings, and stamps, and I
sing with the Brazos Valley Chorale .
I have a substantial interest in history, and
particularly in the history of mathematics. I care very much about space
flight and see it as essential for the future of mankind. I have attended
several launches;

here is a nice picture of a night launch as photographed by my friend Tom Dow. For more about Tom Dow, see Tom's home page. In 1999, I completed 6 years on the Faculty Senate of Texas A&M University. I am married to Barbara J. Hobbs and have two children, Melissa Best and Patty Brunson . We attend St. Andrew's Episcopal Church. I am a member of TACT and of AAUP.

- I am extremely fond of contra, round dancing, and square dancing and
dance with
- Circle Squares, which meets regularly on the first and third Thursday of each month at the A&M Methodist Church starting at 7 pm. Members of the group also often have dance lessons at the same time and place on the second and fourth Thursdays. Matt Barnes is the club caller, but we often have visiting callers.
- Levis and Lace, which meets regularly on the second and fourth Tuesdays of each month at 8 pm in the cafeteria of the school in Gause. This is a plus club. Larry Astle is its caller.
- CONTRA: Often dancing to live music, we have a fine time from 7 until
10 pm on the first Saturday of each month. We meet in the Unitarian Fellowship
Hall at 305 Wellborn Road, College Station. First time dancers enter free;
we ask a $5 donation (students $3) of other dancers. One of the nicer things
about contra is that you don't have to have a partner to participate, and
you don't have to already know how to dance contra. The dance has many
appealing traditional elements. We form in facing lines, and if the dance
is "proper," women are in one line and men in the other. ("Improper"
dances have the men and women alternating in each line.) We are walked
through the figure two or three times until we have understood it, and
then the music starts and we dance for awhile. It's great fun and great
exercise.

Among my favorite callers are the callers for my clubs, Larry Astle and Matt Barnes, but I think very highly of Jim and Fae Park from Arizona. I was extremely fond of Johnnie Wykoff and his wife Star, but sadly Johnnie died suddenly in May, 2000. For those who also loved his calling, Star prepared a list of Johnnie's records.### Education

- B.S. University of Michigan 1962
- Ph.D. University of Waterloo 1971.

### Research Interests

- Graph Theory. My research before entering graduate school was on thickness of graphs. In graduate school and for 10 years after that, I concentrated on Hamiltonian cycles, particularly in squares and higher powers of graphs. I then spent a couple of years working on the Gyarfas and Lehel conjecture that n trees of orders 1 through n can always be packed into K_n. After working on a textbook in linear algebra (Hartfiel and Hobbs, Elementary Linear Algebra, PWS Publishers), I began working with packings of graphs with trees and covering by trees. I did this work with several co-authors, including Paul Catlin, Jerrold W. Grossman, Lavanya Kannan, and Hong-Jian Lai. We 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. We also defined the strength of a graph (following Cunningham) 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. A graph is uniformly dense if eta and gamma are equal. We have characterized uniformly dense graphs. We note that communication in a uniformly dense graph is particularly survivable under attacks on the edges, and so we are interested in constructing such graphs. We have found several classes of uniformly dense graphs and several ways of constructing such graphs.
- Matroid Theory. Both eta and gamma are easily expressed in matroid terms, and so uniformly dense matroids are defined. Many of our results in this subject are most naturally expressed in matroid terms, and so our papers are often papers in matroid theory.
- Selected Publications available.

- Annual reports for 1996 , 1997 , 1998 , 1999 , 2000 ,
2001 , 2002 ,
2003 , 2004 ,
2005 , available.
## ESSAY ON READING RESEARCH PAPERS

I have written an essay on how to read research papers that some people have found interesting. To see that paper, click here , and to download it in AMSTeX, click here .#### Interesting Links

- Math Reviews 2000 subject classifications
- Electronic Research Announcements of the AMS
- MAA
- The travelling salesman problem bibliography is a useful source of information on this problem.
- The newsletter "Concerns of Young Mathematicians" newsletter is interesting to more than just young mathematicians. It talks about jobs, meetings, and how to do one's job. The archives are worth examining.
- Powell's Technical Books , a really great used book store with lots of used advanced mathematics books for sale.
- The Paul Erdos page tells about the Erdos number and names the people who are involved in it. There is also a link to an excellent obituary of Paul, who died on September 20, 1996.
- Photos of the asteroid Eros taken by NEAR are very interesting.
- Novaspace Galleries sells paintings and prints related to space. The pictures at this site are fantastic!
- Abby's Menagerie home page presents an interesting idea.
- Read Shakespeare's works , complete with on-line glossary (of mixed value).
- Some neat archaeological home pages are listed. Most of these links no longer work.
- A very nice list of the academic genealogies of people in mathematical fields related to computer science, such as in combinatorics. Take a look.
- A fascinating spoof by Prof. Sokal together with his explanation can be found aat this web site.
- Mathcamp is a really good
experinece for a bright high school student. Check it out.

*Last updated: May 18, 2010.*