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Research

My research is in combinatorics; more specifically but still broadly speaking, I like graph theory, graph colorings, hypergraphs, competitive optimization, and partially ordered sets.

Publications (and accepted articles):

  • N. Alon, A.V. Kostochka, B. Reiniger, D.B. West, X. Zhu. Coloring, sparseness, and girth. Accepted, Israel J. Math. [arXiv]
  • B. Reiniger and E. Yeager. Large subposets with small dimension. Accepted, Order. [arXiv]
  • A.V. Kostochka and B. Reiniger. The minimum number of edges in a 4-critical graph that is bipartite plus 3 edges. European J. Combin., 46:89-94, 2015. [web]
  • N. Kosar, S. Petrickova, B. Reiniger, and E. Yeager. A note on list-coloring powers of graphs. Discrete Math., 332:10-14, 2014. [arXiv; web]
  • S. Behrens, C. Erbes, M. Ferrara, S.G. Hartke, B. Reiniger, H. Spinoza, and C. Tomlinson. New results on degree sequences of uniform hypergraphs. Electron. J. Combin., 20(4):Paper 14, 2013. [web]
  • B. Collier, E. Kerman, B. Reiniger, B. Turmunkh, and A. Zimmer. A symplectic proof of a theorem of Franks. Compos. Math., 148(6):1969-1984, 2012. [arXiv]

Submitted:

  • C. Cox, M. Ferrara, R. Martin, B. Reiniger. Chv├ítal-type results for degree sequence Ramsey numbers. Submitted. [web]
  • J. Carraher, W. Kinnersley, B. Reiniger, and D.B. West. The game saturation number of a graph. Submitted. [arXiv]

Manuscripts in progress:

  • S. Loeb, T. Mahoney, B. Reiniger, J. Wise. Dynamically coloring graphs with given genus.

As an undergraduate I did some research in combinatorics, particularly Rosa-type graph labelings. I have worked with the combinatorics REGS group here at UIUC each summer since arriving in '09. In the 2010 summer I also worked on a REGS project concerning periodic points of Hamiltonian diffeomorphisms of the two-sphere.

I am broadly interested in most areas of mathematics. Areas that have attracted me most include combinatorics, geometric group theory, some category theory, cohomology of spaces and groups, and number theory.

Last modified January 8, 2015.


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Giving a hypergraphic sequence talk, 2013.