# Our Faculty

## Mark Kayll

Professor

### Contact

- Office
- MATH 209
- Phone
- 406.243.2403
- mark.kayll@umontana.edu
- Office Hours
Tuesday 11:00--11:50am, Thursday 12:20--1:10pm, and by appointment

### Education

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, The Erdös-Faber-Lovász Conjecture: Fifty Exciting Years,
*Mathematics Magazine, to appear* - D. Johnston, P.M. Kayll, and C. Palmer, Deranged matchings: proofs and conjectures,
*American Mathematical Monthly***131****(2)**(2024), 95-111 - P.M. Kayll and M. Morris, On colouring oriented graphs of large girth,
*Contributions to Discrete Mathematics***18(2)**(2023), 234–243 - 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 - 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-SiO
_{2}films,*Physical Review B***31**(1985), 5113–5120

### Affiliations

AMS, CMS, MAA, ICA (Elected Member of ICA Council, 2017–2026)

### Professional Experience

Supervised/co-supervised the doctoral dissertations of five students; see the **Math Genealogy Project **for details.

### Honors / Awards

- Provost’s Distinguished Faculty Lecturer, 2013
- Carl B. Allendoerfer Award, Mathematical Association of America, 2012
- Canadian Achievers Dinner guest, by invitation of Prime Minister Pierre Elliott Trudeau, in the presence of Queen Elizabeth II, on the occasion of the Proclamation of the Constitution Act, 1982
- Governor General’s Bronze Medal, Canada, 1981