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Colourings and Flows in Graphs
NSF
About This Grant
In combinatorial mathematics, a graph is a set of points, some of which may be joined by lines. Graphs are useful models for electrical grids, chemical structures, the internet, transportation maps, and many other objects -- anything that can be viewed as a network is, abstractly, a graph. Real world problems involving such networks benefit from the theorems, algorithms, and insights of graph theory. The PI is most interested in graph problems involving so-called colourings and flows, and this project focuses on three sub-problems within these topics. Graduate students will be mentored as part of this project. The three sub-projects prioritized in this proposal are titled: flows with boundary conditions in graphs; clique subgraphs and strong colouring, and; total colouring and overfullness in graphs with large maximum degree. The first of these is about developing concepts for use as inductive tools towards Tutte's Flow Conjectures. The second is an attack on the Strong Colouring Conjecture, using a clique reduction technique. The third and final sub-project seeks to prove a special case of the Overfull Conjecture (involving large graphs with large maximum degree) and to use this work towards the Total Colouring Conjecture. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Grant Summary
Colourings and Flows in Graphs is a NSF grant providing up to $265K for university, nonprofit, small business. Applications are due 2028-08-31 (open). Check eligibility and apply with FindGrants.
Focus Areas
Eligibility
How to Apply
Up to $265K
2028-08-31
- 1Confirm your organization is eligible for Colourings and Flows in Graphs from NSF, checking organization type, location, and any population or project requirements.
- 2Gather the required documents and information, including your organization details, project plan, and budget figures.
- 3Draft your application narrative and budget addressing the funder's priorities and review criteria. FindGrants can draft each section for you to review and edit.
- 4Review every section against the requirements checklist, then export a submission-ready application pack and submit it to NSF before the deadline.
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Colourings and Flows in Graphs: Frequently Asked Questions
Who is eligible for the Colourings and Flows in Graphs?
Colourings and Flows in Graphs is offered by NSF and is generally open to university, nonprofit, small business. It is open to organizations nationwide unless the funder specifies otherwise. Review the specific eligibility terms before applying, since funders set their own requirements around organization type, location, and the population or project being served.
How much funding does the Colourings and Flows in Graphs provide?
Colourings and Flows in Graphs provides up to $265K per award from NSF. Actual award sizes depend on the scope of your project, available program funds, and the number of applicants, so build a budget that reflects realistic, allowable costs rather than the maximum figure.
When is the Colourings and Flows in Graphs deadline?
Applications for Colourings and Flows in Graphs are due 2028-08-31 (open). Because deadlines can change, verify the date with the funder, NSF, and give yourself enough time to prepare a complete, competitive application before the close date.
How do you apply for the Colourings and Flows in Graphs?
To apply for Colourings and Flows in Graphs, confirm your eligibility, gather the required documents, and prepare a narrative and budget that address the funder's priorities. FindGrants guides you step by step and can draft each section, then exports a submission-ready application pack for this grant from NSF.