64th Annual STS (2004-2005)
Finalists
Robert Thomas Cordwell
NEW MEXICO
Robert Thomas Cordwell, 17, of Albuquerque, submitted his mathematics
project for the Intel Science Talent Search in graph theory. Bob's project
considers ways to partition the complete graph Kn on n vertices into subgraphs;
he considers edge partitions, one in which each edge of Kn lies in exactly one
subgraph. To describe this, he represents Kn as the vertices of a regular
polygon with n sides, joining all the vertices with straight lines. He requires
all subgraphs to be cycles, which is only possible when n is odd. A cycle which
does not intersect itself is called inclusive if it goes around the center of
the n-gon; otherwise it is exclusive. Bob proves that Kn can be partitioned into
inclusive cycles of lengths 3 and 4 for any odd n. If n + 1 or n - 1 is
divisible by 8, he shows that Kn can be partitioned into exclusive 3-cycles as
well. Bob, who has perfect SAT scores, is first in his class of 343 at Manzano
High School. A second generation Eagle Scout, he has won numerous awards,
including the Rensselaer Medal. The son of Dr. William and Rosemary Cordwell,
Bob plans to double major in mathematics and computer science at the University
of Chicago.
