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Maple League Mid-term Progress Report – Mathematical Graph Theory

Investigators: Dr. Margaret-Ellen Messinger (Mount Allison), Dr. Stephen Finbow (St. FX), Dr. Nancy Clarke (Acadia)

The Maple League funded nine projects in 2019/2020 to promote and facilitate collaborative research, innovative teaching, spring and international field study programs, and travel amongst the four campuses. We are delighted to share, in a series called the Maple League Funding Spotlight, progress reports from these projects. We are particularly interested in the insights and impact these funded projects have had on their communities in the time of COVID. We had a chance to sit down with Dr. Stephen Finbow from St. Francis Xavier University to talk about this project and learn more about collaboration across the four universities.

JESSICA RIDDELL (EXECUTIVE DIRECTOR OF THE MAPLE LEAGUE): The guiding question that animates all our Maple League collaborations is: “What can we do together that we cannot do on our own?” How does this resonate with the project you’ve undertaken?

DR. STEPHEN FINBOW, CO-INVESTIGATOR (ST. FX): Mathematics is an extremely rigorous area of research that demands a high level of intellectual strength in terms of pushing to understand and solve relevant problems, in addition to determination and internal discipline to continuously refine and improve upon solutions. The sharing of our team’s knowledge and expertise is the engine that encourages creativity, blossoms new approaches, deepens the understanding of problems, expands results, and accelerates the dissemination of our findings. Our teamwork collaboration encouraged us to use the breadth of knowledge we each brought to the project to think about things differently, to be agile in our techniques, and to make connections we didn’t know existed. By working together, we were able to deepen the intellectual understanding of the project and solve the problems more efficiently, and our work is better for it.

Furthermore, this project promotes equity, diversity and inclusion in academia. Two of the three researchers were renowned female scholars acting as outstanding mentors to the summer research assistant who was also female. This is especially important in promoting gender equity in a field that historically has been male dominant.

JR: How does your project benefit from working and learning in relationship-rich environments?

SF: The synergistic relationship has accelerated our progress, expanded our range of results, and enhanced the quality of research in Hyperopic Cops and Robbers realizing our two main objectives.

The development of robust relationships between Maple League researchers, departments and institutions, and their students helps to support the necessary depth of expertise necessary for successfully solving problems and undertaking large projects. This is especially critical as primarily undergraduate universities typically will not have the breadth of researchers in a specific field compared to larger institutions and programs such as mathematics where upper year enrollments are traditionally smaller. The support from the Maple League helps to eliminate this challenge, providing a vehicle that develops relationships that bring world-class expertise together, accelerating the expansion of our knowledge in the field while also providing a more equitable balance between research collaboration opportunities within smaller institutions versus larger institutions.

JR: What kind of impact do you hope to have — on your own work, on institutional cultures, or beyond the academy — with your project?

SF: The project has had a profound impact on our HQP student training. The innovative approach of having three co-supervisors provided an unparalleled experience for the student, exposing her to multiple researchers. This ultimately led to a deeper understanding of the research and resulted in her achievement in winning second place for her research talk at the Science Atlantic 2020 conference.

Furthermore, the student participated in problem solving and interacted in team building activities with other HQP at the other institutions. This strengthened the relationship between the students and departments.

The investment of funds by the Maple League has turned what could have been a superficial agreement into a catalysis for success. As one of the pathfinders in this innovative model between the four universities, I believe we have sparked the attention of many other researchers to seek opportunities to formalize solid collaborations between the institutions to realize results for themselves, their students, and their departments.

JR: Has the global pandemic affected your project and/or your understanding of collaboration? If so, why? If not, why?

SF: The global pandemic has had both positive and negative impacts on the project.

Positives: Due to the rapid shutdown of universities, travel restrictions and social distancing requirements, the methodology of the collaborative in-person project had to immediately transition to online. Virtual communication was used exclusively by the researchers throughout the entire project. Previously there existed in many areas of academia a bias against the value of virtual collaboration. Although it is not as efficient as face-to-face interaction, the research team worked tirelessly together remotely to push the project forward which redeemed results for all. By being flexible, adapting to the new landscape, and undertaking the learning of new technology to make it feasible, we were able to continue with the goals of this project. I believe this grant helped to push us through the barriers and we have emerged more resilient and better prepared to face future challenges that may impact research productivity.

Negatives: The massive disruption of abruptly moving from in-person teaching to a remote learning environment at the end of term put incredible strain on all researchers as they grappled with these significant challenges. Furthermore, two of the three researchers were department chairs. The pandemic put an immense pressure and fatigue on chairs’ time and availability as universities tried to navigate through unchartered situations. The research team continued to meet weekly through the summer; however, the unprecedented time pressures the chairs faced created substantial disruptions to the rhythm of research and limited the hours available to meet the project’s aggressive timeline goals. The pandemic hindered the dissemination of results schedule. The adjusted timeline includes the submission for peer-reviewed publication in the spring 2021 and presentation of the results at a (online) conference during the summer of 2021. The team was able to meet the goal of having the HQP well-prepared to present results at the Science Atlantic (fall 2020) conference, where she won second prize

Interested in learning more? Here is a brief description of the project:

In graph searching models, a subfield of mathematical graph theory, we envision the occurrence of an intruder in a network. The network can be many things such as city streets or a computer network. A set of agents move around the network with a goal of capturing the intruder. Generally, it is important to determine the minimum number of agents required to guarantee capture of a mobile intruder, the “cop number”.

In “Hyperopic Cops and Robbers”, the information accessible to agents is restricted: agents can view the intruder’s location except when the intruder is nearby. Motivation for this model comes from emulating certain prey-predator systems, where the prey (the robber) has short-range anti-predatory defense (e.g. squid releasing colored ink).

Hyperopic Cops and Robbers was recently introduced (A. Bonato, N.E. Clarke, D. Cox, S. Finbow, F. Mc Inerney, M.E. Messinger, “Hyperopic Cops and Robbers” in Theoretical Computer Science) with results for countable graphs, planar graphs, and graphs with restricted diameter.

This project built upon this and studied Hyperopic Cops and Robbers with three primary objectives:

– Determining the cop number for particular families of graphs;

– Identifying general strategies and establishing bounds on the exact value of the cop number; and

– Identifying the relationship between the cop number of input graphs and the cop number of a product graph.

Contact us:

For more information about this project, contact. Dr. Stephen Finbow at

For more information on funding opportunities, visit:

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