(i,j)-step competition graphs

Researchers: Max Black and Carissa Babcock

Mentor: Dr. Kim A.S. Factor

Background

Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Competition graphs are, essentially, graphs

Objectives

During this project, we will examine and explore the following:

1. Previous research regarding competition graphs and (1,2)-step competition graphs of food webs
2. Competition graphs and (1,2)-step competition graphs of a specific food web

Additionally, we will further previous research by doing the following:

1. Furthering research on (i,j)-step competition graphs by exploring new theory and computation
2. Applying competition graphs and (i,j)-step competition graphs in new areas

A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click here.

Week	Description
Week 1 (5/30/17-6/2/17): Orientation and Introductions	Complete the education mdule, The Biology and Mathematics of Food Webs, by Thursday, 6/1/17 Attend the talk at 11:00PM in CU 401 Enter the title, description and milestones/goals into the wiki by Friday, 6/2/2017, by midnight Update Wiki at end of week or during week to reflect on what has been accomplished Read (1,2)-step competition graph of a tournament and have questions ready for Wednesday, 6/7/2017
Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples	Meeting Wednesday, 6/7, with mentor Discuss the paper from last week--prepare to answer questions and/or ask them Begin reading Kaitlyn Ryan's master's thesis to explore biological background, mathematical background, and statistical information for the topic. Make notes and questions for Thursday's meeting Begin reading A Characterization of Competition Graphs Attend Ethics training at 9:00AM on 6/6 in CU 401 Participate in the talk and luncheon at 11:30AM on 6/8, CU 401 Start comparing competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating our own small food web examples Learn LaTex (Carissa--Max can tutor) Update Wiki at end of week or during week to reflect on what has been accomplished
Week 3 (6/12/17-6/16/17): Formulating Research Questions	Mentor meeting on Tuesday, 6/13 Mentor meeting on
Week 4 (6/19/17-6/23/17):	Create appropriate network connections to the cloud and/or to devices in the same Wifi network Work on presentation
Week 5 (6/26/17-6/30/17):
Week 6 (7/3/17-7/7/17):
Week 7 (7/10/17-7/14/17):
Week 8 (7/17/17-7/21/17):
Week 9 (7/24/17-7/28/17):
Week 10 (7/31/17-8/4/17):