Atif Abueida, PhD

My predominant area of research is Discrete Mathematics with primary emphasis on Graph Theory and Combinatorial Design Theory. My secondary area of research is Complex Variables with emphasis in the location of zeros of polynomials with complex coefficients.

Papers published and in progress:

• Multidesigns for graphs-pairs on 4 and 5 vertices (with Mike Daven), Graphs and Combinatorics 19 (4), 2003, 433-447.

• Multidecompositions of the complete graph (with Mike Daven), Ars Combinatoria 72, 2004, 17-22.

• Determining properties of a Multipartite Tournament from its Lattice of Convex Subsets (with Wiebke Diestelkamp, Stephanie Edwards, and Darren Parker), Australasian Journal of Combinatorics 31, 2005, 217-230.

• Multidesigns of the λ-fold complete graph (with Mike Daven and Ken Roblee), Australasian Journal of Combinatorics 32, 2005, 125-136.

• A note on the recognition of bisplit graphs (with R. Sritharan), Discrete Mathematics 306 (17), 2006, 2108-2110.

• Cycle extendability and Hamilton cycles in chordal graph classes (with R. Sritharan), SIAM Journal on Discrete Mathematics 20 (3), 2006, 669-681.

• Multipacking and Multicovering of K_n-F with Graph-Pairs of Order 5 where F is a Hamilton Cycle or (almost) 1-Factor (with Christian Hampson), Congressus Numerantium, 183, 2006, 11-32.

• Multidesigns for graph-triples of order 6, (with Mike Daven, Wiebke Diestelkamp, Stephanie Edwards, and Darren Parker), Congressus Numerantium, 183, 2006, 139-160.

• Multidecomposition of λ K_m into small Cycles and Claws (with Theresa O'Neil), Bulletin of the Institute of Combinatorics and its Applications, 49, 2007, 32-40.

• Some Results on the Location of Zeros of Polynomials (with Robert Gardner), Theory of Polynomials and Applications, Recent Advances, Deep & Deep Publications, India, 2007.

• Multidecomposition of the complete graph into graph pairs of order 4 with various leaves (with Sally Clark and David Leach), Ars Combinatoria, to appear.

• Multidecomposition of K_n-F into Graph-Pairs of Order 5 where F is a Hamilton Cycle or (almost) 1-Factor (with Christian Hampson), Ars Combinatoria, to appear.

• Multidesigns of the complete graph with a hole into the graph-pair of order 4, Bulletin of the Institute of Combinatorics and its Applications, to appear.

• Uniform k-Distant Even Trees are Harmonious, (with Dan Roberts), Utilitas Mathematica, to appear.

• (a,b)-domination: A unified framework for some domination parameters, (with Robert Rublacaba and Matthew Walsh), Submitted.

• Inverse spread limit of a nonnegative matrix, (with Mark Nielsen and Tin-Yau Tam), Submitted.

• Centrality and anticentrality (DIMACS teaching module, with Mike Ackerman and Sul-Young Choi), submitted.

• New heterogeneous decompositions into spanning trees (with Andrew Blinco, Sally Clark, Mike Daven and Roger Eggleton), in preparation.

Invited Colloquia, Contributed Conference Presentations and Professional Activities:

• Keynote speaker: ``Centrality and AntiCentrality on Trees", TROY MathFest, Troy University, March 2006.

• Invited speaker: ``Cycle Extension and Hamilton Cycles'', Indian University-Purdue University-Fort Wane, May 2005.

• Invited talk: ``Discrete Mathematics Workshops at the University of Dayton", Ohio NExT Meeting, Miami University, April 2005.

• Invited talk: ``Multidecomposition of the Complete Graph with Various Leaves", AMS Southeastern Sectional Meeting, Western
  Kentucky University, March 2005.

• Invited Speaker:`` Decomposition and Multidecomposition of the Complete Graph'', Wright State University, February 2005.

• Invited speaker:  ``Cycle Extension and Hamilton Cycles", Stevens Institute of Technology, November 2004.

• Invited speaker:  ``What a small world", Mount Saint Mary College, November 2004.

• Invited talk: ``Cycle extendability and Hamilton cycles in chordal graph classes'', The 17th  Cumberland Conference on Combinatorics, Graph Theory, and Computing, May 2004.

• Contributed talk: ``Cycle extendability and Hamilton cycles in chordal graph classes'' Thirty-fifth Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, FL, March 2004.

• Contributed talk: ``Multidesigns of multipartite graphs'' Joint Mathematics Meetings, Phoenix, AR January 2004.

• Contributed talk: `` Multidesigns of the λ-fold Complete Graph'' Miami University, Miami, OH, September 2003.

• Guest speaker: ``It is a small world after all'', Mathematics Club, University of Dayton, September 2003.

• Contributed paper: ``Multidesigns of the λ-fold Complete Graph'', Midwest Graph Theory Conference, September 2003.

• Invited speaker: ``The Full Embedding Problem'', Wright State University, March 2002.

• Contributed paper: ``Multidecomposition of the complete graph", Joint Mathematics Meetings, San Diego, January 2002.

• Contributed paper:  ``Multidecomposition of the complete graph", Midwest Graph Theory Conference, October 2001.

• Invited speaker: ``Multidecomposition of the complete graph'', Youngstown State University, May 2001.

• Contributed paper: ``Multidecomposition and Multifactorization'', New York Graph Theory Day, November 2000.

• Contributed paper: ``The Full Embedding Problem'', Ninth International Conference, GTCC 2000, Western Michigan University, June 2000.

• Invited speaker: ``The Full Embedding Problem'', Southwestern Oklahoma State University, March 2000.