Arthur H Busch

Associate Professor

Full-Time Faculty


Arthur Busch received his B.A. in 1997 from the University of Washington, and worked as a programmer in the investment and oil and gas industry in Denver. He received his Ph.D. in 2005 from the University of Colorado, Denver. After working for one year as a post-doc at Lehigh University, Arthur joined the faculty of the Department of Mathematics at UD in 2006.


  • B.A., 1997, University of Washington
  • Ph.D., 2005, University of Colorado Denver

Research Interests

  • Graph Theory
  • Combinatorics

Selected Presentations

"Arc-traceable tournaments and digraphs," (invited) Paths, Cycles and Graph Structures Workshop, University of Colorado Denver, July 2009.

"Anti-cycles in directed graphs," (invited) 2009 SIAM Annual Meeting, Denver CO, July 2009.

"Tournament score sequences with partition k-transitive realizations," (invited) 2nd Canadian Discrete and Algorithmic Mathematics Conference, Montreal PQ, May 2009.

"Recognition Algorithms for some generalizations of interval graphs," (invited) Mathfest 2008, Madison WI, July 2008.

"Recognizing a special class of interval bigraphs," (invited) 2008 Joint Mathematics Meetings (of the AMS and MAA), San Diego CA, January 2008.

"Recognizing bipartite tolerance graphs in linear time," 33rd International Workshop on Graph Theoretic Concepts in Computer Science, Dornburg Germany, June 2007.

"Finding chain covers of chordal-bipartite graphs," (invited) Eastern Section Meeting of the AMS, Stevens Institute of Technology, April 2007.

"Transitive subtournaments of tournaments with a given score sequence," Mathematics Department Colloquium, Miami University, February 2007.

"Hamiltonian paths and cycles in tournaments," Mathematics Department Colloquium, Wright State University, September 2006.

"Recognizing Bipartite Tolerance Graphs and Probe Interval Graphs," Mathematics Colloquium, Lehigh University, February 2006.

Selected Publications

Atif Abueida, Arthur H. Busch, and R. Sritharan. "A min-max property of chordal bipartite graphs with applications." To appear in Graphs and Combinatorics.

Arthur H. Busch, Guantao Chen, and Michael S. Jacobson. "Transitive partitions in realizations of tournament score sequences." To appear in J. Graph Theory.

Arthur H. Busch and Michael S. Jacobson. "Extremal results on arc-traceable tournaments." J. Combin. Math. Combin. Comput., 63:3–15, 2007.

Arthur H. Busch and Garth Isaak. "Recognizing bipartite tolerance graphs in linear time." In Graph-theoretic concepts in computer science, volume 4769 of Lecture Notes in Comput. Sci., pages 12–20, 2007.

Arthur Busch, Michael Ferrara, and Nathan Kahl. "Generalizing -graphs." Discrete Appl. Math., 155(18):2487–2495, 2007.

David E. Brown, Arthur H. Busch, and J. Richard Lundgren. "Interval tournaments." J. Graph Theory, 56(1):72–81, 2007.

Arthur H. Busch, Michael S. Jacobson, and K. B. Reid. "On arc-traceable tournaments." J. Graph Theory, 53(2):157–166, 2006.

Arthur H. Busch. "A note on the number of Hamiltonian paths in strong tournaments." Electron. J. Combin., 13(1):Note 3, 4 pp. (electronic), 2006.

Arthur H. Busch. "A characterization of triangle-free tolerance graphs." Discrete Appl. Math., 154(3):471–477, 2006.

Arthur H. Busch, Michael S. Jacobson, and K. Brooks Reid. "On a conjecture of Quintas and arc-traceability in upset tournaments." Discuss. Math. Graph Theory, 25(3):345–354, 2005.