General Contributed Paper Session 7

Salon H

1:15p.m. - 5:45p.m.

 

Here are the abstracts for the new papers mentioned in Saturday's What's New at MathFest?.

 

On The Number of Vertices of a Tashkinov Tree

Oguz Kurt, Ohio State University

 In optimization problems, the fractional solution is usually found in polynomial time while the integer solution many times ends up NP-complete. In 1967, Gupta and later Goldberg asked the following question for a multi-graph : "What is the smallest function  of , the maximum degree of a graph, such that if then , where and denote the chromatic index and fractional chromatic index of ?". They also conjectured that . In 2000, Tashkinov found a very nice tree algorithm that finds a subgraph of which almost satisfies the conjecture their conjecture. Since then the so-called Goldberg-Gupta Conjecture is studied more than its earliest days. In 2006, Scheide showed that "If the number of vertices, , of a largest Tashkinov tree in is less than 11  then is elementary" meaning that Goldberg-Gupta Conjecture holds. We show that is elementary whenever improving the result of Scheide. Moreover, together with another result of ours, this gives the best known function such that if then  .

 

Expanding Research Horizons through Mathematical Biology

Jennifer Galovich, St. John's University and College of St. Benedict, and Thomas Sibley, St. John's University

In our experience, problems in mathematical biology attract a wide variety of mathematics students. Moreover, mathematics investigations inspired by questions from biology can make use of a range of mathematical ideas and techniques.  We will discuss examples from recent student research to show that ideas from discrete mathematics are proving to be more and more useful -- it's not just differential equations any more!