Mark Kayll

Mark Kayll


Office: MATH 209
Email: mark.kayll@umontana.edu
Office Hours:

Tuesday 3:00 -- 3:45pm and Thursday: 2:00 -- 2:50pm; and by appointment (informal or otherwise)

Please see course syllabus for information; if you are not registered for one of my courses, please send an email request.


B.Sc. in Mathematics and Statistics, Simon Fraser University
Ph.D. in Mathematics, Rutgers University

Research Interests

Discrete Mathematics, Optimization, Theoretical Computer Science

Selected Publications

  • P.M. Kayll and E. Parsa, Uniquely D-colourable digraphs with large girth II: simplification via generalization, Electronic Journal of Combinatorics 28(1) (2021), #P1.48
  • E. Parsa and P.M. Kayll, On random digraphs and cores, Australasian Journal of Combinatorics 79 (2021), 371–379
  • P.M. Kayll and D. Perkins, On lengths of burn-off chip-firing games, Journal of Combinatorial Mathematics and Combinatorial Computing 116 (2021), 53–78
  • D. Perkins and P.M. Kayll, A chip-firing variation and a Markov chain with uniform stationary distribution, Australasian Journal of Combinatorics 68 (2017), 330–345
  • P.M. Kayll, Two chromatic conjectures: one for vertices and one for edges, Chapter 11 in Graph Theory  Favorite Conjectures and Open Problems 1 (R. Gera, S.T. Hedetniemi, and C.E. Larson, eds.), pp. 171–194, Problem Books in Mathematics, Springer International, Switzerland, 2016
  • P.M. Kayll, Deranged matchings: enumeration by integration!!, American Mathematical Monthly 122 (2015), 51
  • A. Harutyunyan, P.M. Kayll, B. Mohar and L. Rafferty, Uniquely D-colourable digraphs with large girth, Canadian Journal of Mathematics 64 (2012), 1310–1328
  • P.M. Kayll, Integrals don’t have anything to do with discrete math, do they?, Mathematics Magazine 84 (2011), 108–119
  • P.M. Kayll, König-Egerváry graphs are non-Edmonds, Graphs and Combinatorics 26 (2010), 721–726
  • P.M. Kayll, A note on weak Sidon sequences, Discrete Mathematics 299 (2005), 141–144
  • D. Bokal, G. Fijavz, M. Juvan, P.M. Kayll and B. Mohar, The circular chromatic number of a digraph, Journal of Graph Theory 46 (2004), 227–240
  • S.P. McAlister, A.D. Inglis and P.M. Kayll, Conduction in cosputtered Au-SiO2 films, Physical Review B 31 (1985), 5113–5120


Home Department

Mathematical Sciences

Area of Expertise

Discrete Mathematics (Combinatorics and Graph Theory); Mathematics of Finite Sets and Graph Models


AMS, CMS, MAA, ICA (Elected Member of ICA Council, 2017–2023)