UM Directory

Research Interests

Discrete Mathematics, Optimization, Theoretical Computer Science

Selected Publications

• P.M. Kayll, The Erdös-Faber-Lovász Conjecture: Fifty Exciting Years, Mathematics Magazine 98(4) (2025), to appear
• P.M. Kayll and C.E. Larson, Egerváry graphs: Deming decompositions and independence structure, Journal of Combinatorics 16(2) (2025), 141-180
• 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-SiO₂ 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 six 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

Home Department

Mathematical Sciences

Area of Expertise

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