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Abstract

A graph can be embedded in various spaces. This paper examines S1 embeddings of graphs. Just as links can be defined in spatial embeddings of graphs, links can be defined in S1 embeddings. Because linking properties are preserved under vertex expansion, there exists a finite complete set of minor minimal graphs such that every S1 embedding contains a non-split 3-link. This paper presents a list of minor minimal intrinsically S1 3-linked graphs, along with methods used to find and verify the list, in hopes of obtaining the complete minor minimal set. Other aspects of S1 embeddings are also examined. 1

Author Bio

Andrew F. Brouwer is a member of the class of 2009 at SUNY College at Potsdam. He is a mathematics and chemistry major and literature minor. Andrew participated in the joint Clarkson and SUNY College at Potsdam REU in the summer of 2006 and in the Environnmental Science Institute at UT Austin REU in the summer of 2007.

Rachel M. Davis graduated with the class of 2007 of Le Moyne College with a degree in mathematics. Rachel has participated in George Washington University�s SPWM program in the summer of 2005 and in the joint Clarkson and SUNY College at Potsdam REU in the summer of 2006. She attended the Penn State MASS program in the fall of 2006 and is now in a mathematics Ph.D. program at the University of Wisconsin-Madison.

Abel J. Larkin graduated with the class of 2007 of SUNY College at Potsdam with a mathematics and secondary education degree. Abel participated in the joint Clarkson and SUNY College at Potsdam REU in the summer of 2006. He is currently teaching High School Math at Faith Fellowship Christian School in Watertown, New York.

Daniel H. Studenmund is a member of the class of 2008 at Haverford College. He is a mathematics major. Daniel participated in the joint Clarkson and SUNY College at Potsdam REU in the summer of 2006 and studied at the Budapest Semesters in Mathematics program in the spring of 2007.

Cherith A. Tucker graduated with a degree in mathematics from Southern Nazarene University in May 2007. Cherith participated in Carleton College�s Summer Math Program for Women in the summer of 2005 and in the joint Clarkson and SUNY College at Potsdam REU in the summer of 2006. She is currently enrolled in the mathematics PhD program at the University of Oklahoma.

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