Thomas Murff

Thomas Murff is currently an affiliate researcher at the Wolfram Institute, working on theoretical mathematics relating to hypergraph theory, by applying novel tools combining order theory, universal algebra, and combinatorial techniques. His current interest involves studying spaces of hypergraph colorings as mappings, their interrelations, and the associated space of automorphism/color-preserving groups. Thomas holds a BA in mathematics from Vassar College, and is a graduate of the Wolfram Summer School 2024. He is currently applying to graduate school for a pure math PhD program.

Research Interests

  • Hypergraph Theory

  • Order theory and universal algebra

  • Spaces of hypergraph colorings

  • Automorphism and color-preserving groups

Research Output

Featured
Upper Bounds on the Chromatic Index of Linear Hypergraphs
Upper Bounds on the Chromatic Index of Linear Hypergraphs

Thomas Murff, Xerxes D. Arsiwalla

This work studies upper bounds on the chromatic index of linear, loopless hypergraphs. The first bound is derived using a color-preserving group acting on a properly and minimally edge-colored hypergraph, where the group’s orbits create a finer partition of the coloring. This provides an upper bound on the chromatic index. The following results examine combinatorial properties of hypergraph coloring and outline a possible approach to the Berge–Füredi conjecture, linking the chromatic index to the maximum degree of the associated graph plus one. Three sufficient conditions are also identified for the conjecture to hold, involving the Helly property for hypergraphs.

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