John Engbers
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My research currently lies in discrete mathematics, combinatorics, and graph theory. Recently I've been looking at enumerative and structural questions related to graph homomorphisms, or H-colorings, of fixed graphs and classes of graphs. I've also been looking at a class of extremal problems for independent sets in graphs and several related extremal questions that deal with H-colorings.

Papers: (* indicates undergraduate student)

  1. Extremal graphs for average sizes of maximal matchings
    (with Aysel Erey) Submitted
  2. Maximizing the number of H-colorings of graphs with a fixed minimum degree
    Submitted
  3. Tomescu's graph coloring conjecture for l-connected graphs
    (with Aysel Erey, Jacob Fox, and Xiaoyu He), SIAM Journal on Discrete Mathematics 35(2) (2021), 1478-1502.
  4. Independent sets in n-vertex k-chromatic l-connected graphs
    (with Lauren Keough and Taylor Short) Discrete Mathematics 344 (2021), 112376.
  5. Inextricably linked: a trigonometric coupling
    (with Adam Hammett and Ian Hogan) Mathematics Magazine 93(5) (2020), 352-362.
  6. To Replace or Not To Replace - That Is The Question
    (with Adam Hammett) College Mathematics Journal 51(2) (2020), 117-123.
  7. Colored multipermutations and a combinatorial generalization of Worpitzky's identity
    (with Jay Pantone and Christopher Stocker) Australasian Journal of Combinatorics 78(2) (2020), 335-347.
  8. Silos, snow cones, railroad spikes, and spherical coordinates
    (with Adam Hammett) Mathematics Magazine 93(2) (2020), 143-147.
  9. The n-children problem
    (with Adam Hammett) College Mathematics Journal 50(4) (2019), 242-249.
  10. Problem 1146
    (with Adam Hammett) College Mathematics Journal 50(2) (2019), p. 143.
  11. Maximizing and minimizing the number of generalized colorings of trees
    (with Christopher Stocker) Discrete Mathematics 342 (2019), 1048-1055.
  12. Restricted Stirling and Lah number matrices and their inverses
    (with David Galvin and Cliff Smyth) Journal of Combinatorial Theory, Series A 161 (2019), 271-298.
  13. Extremal colorings and independent sets
    (with Aysel Erey) Graphs and Combinatorics 34 (2018), 1347-1361.
  14. Combinatorial proofs of identities of Alzer and Prodinger and some generalizations
    (with Christopher Stocker) Integers 18 (2018), #A49.
  15. On comparability of bigrassmannian permutations
    (with Adam Hammett) Australasian Journal of Combinatorics 71(1) (2018), 121-152.
  16. Merging peg solitaire on graphs
    (with Ryan Weber*) Involve 11-1 (2018) 53-66.
  17. Maximizing H-colorings of connected graphs with fixed minimum degree
    Journal of Graph Theory 85 (2017) 780-787.
  18. Extremal H-colorings of trees and 2-connected graphs
    (with David Galvin) Journal of Combinatorial Theory, Series B 122 (2017) 800-814.
  19. A direct proof of the integral formulae for the inverse hyperbolic functions (Classroom Capsule)
    (with Adam Hammett) College Mathematics Journal 47(4) (2016) 297-299.
  20. Two combinatorial proofs of identities involving sums of powers of binomial coefficients
    (with Christopher Stocker) Integers 16 (2016) #A58.
  21. Reversible peg solitaire on graphs
    (with Christopher Stocker) Discrete Mathematics 338 (2015) 2014-2019.
  22. Extremal H-colorings of graphs with fixed minimum degree
    Journal of Graph Theory 79 (2015) 103-124.
  23. Combinatorially interpreting generalized Stirling numbers
    (with David Galvin and Justin Hilyard) European Journal of Combinatorics 43 (2015) 32-54.
  24. Trivial meet and join within the lattice of monotone triangles
    (with Adam Hammett) Electronic Journal of Combinatorics 21(3) (2014) #P3.13.
  25. Counting independent sets of a fixed size in graphs with a given minimum degree
    (with David Galvin) Journal of Graph Theory 76 (2014) 149-168.
  26. H-coloring tori
    (with David Galvin) Journal of Combinatorial Theory, Series B 102 (2012) 1110-1133.
  27. H-colouring bipartite graphs
    (with David Galvin) Journal of Combinatorial Theory, Series B 102 (2012) 726-742.
  28. Constructing PL 2-knot complements
    (with Jonathan Dent and Gerard Venema) Proceedings of the 22nd Workshop in Geometric Topology, Colorado College (2005).

Dissertation:

Slides from presentations: (These slides are from the presentation listed - if you saw a different version of the talk and would like those slides instead, please send me an email)