Lucas Mol
Assistant Teaching Professor
Department of Mathematics and Statistics, Thompson Rivers University


Research
Preprints Submitted for Publication
 A. Baranwal, J. D. Currie, L. Mol, P. Ochem, N. Rampersad, and J. Shallit,
Antisquares and critical exponents, September 2022.
arXiv
 J. D. Currie, L. Mol, N. Rampersad, and J. Shallit,
Extending Dekking's construction of an infinite binary word avoiding abelian 4powers, November 2021.
arXiv
Publications
 L. Mol, O. R. Oellermann, and V. Oswal,
On average (edge)connectivity of minimally k(edge)connected graphs, Bulletin of the ICA 94, 95110 (2022).
DOI
arXiv
Supplemental Files: Sage Jupyter Notebook (.ipynb),
Printout of Notebook (.pdf)
 R. M. Casablanca, P. Dankelmann, W. Goddard, L. Mol, and O. R. Oellermann,
The maximum average connectivity among all orientations of a graph, Journal of Combinatorial Optimization 43, 543570 (2022).
DOI
arXiv
 L. Mol and N. Rampersad,
Lengths of extremal squarefree words, Contributions to Discrete Mathematics 16(1), 819 (2021).
DOI
arXiv
Supplemental Files: Short Extremal SquareFree Words,
Short Extremal SquareFree Circular Words
 J. D. Currie and L. Mol,
The undirected repetition threshold and undirected pattern avoidance, Theoretical Computer Science 866, 5669 (2021).
DOI
arXiv
 L. Mol, M. J. H. Murphy, and O. R. Oellermann,
The threshold dimension and irreducible graphs, Discussiones Mathematicae Graph Theory, online ready, 2021.
DOI
arXiv
 B. Cameron and L. Mol,
On the mean subtree order of graphs under edge addition, Journal of Graph Theory, online ready, 2021.
DOI
arXiv
 R. M. Casablanca, L. Mol, and O. R. Oellermann,
Average connectivity of minimally 2connected graphs and average edgeconnectivity of minimally 2edgeconnected graphs,
Discrete Applied Mathematics 289, 233247 (2021).
DOI
arXiv
 J. I. Brown, C. J. Colbourn, D. Cox, C. Graves, and L. Mol,
Network reliability: Heading out on the highway, Networks 77(1), 146160 (2021).
DOI
 L. Mol, N. Rampersad, and J. Shallit,
Extremal overlapfree and extremal \(\beta\)free binary words, Electronic Journal of Combinatorics 27(4), Article P4.42 (2020).
DOI
arXiv
 L. Mol and N. Rampersad,
The weak circular repetition threshold over large alphabets, RAIRO  Theoretical Informatics and Applications 54, Article 6, 2020.
DOI
arXiv
 L. Mol, M. J. H. Murphy, and O. R. Oellermann,
The threshold dimension of a graph, Discrete Applied Mathematics 287, 118133 (2020).
DOI
arXiv
 J. I. Brown and L. Mol,
On the roots of the subtree polynomial, European Journal of Combinatorics 89, (2020).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
The repetition threshold for binary rich words, Discrete Mathematics and Theoretical Computer Science 22(1), (2020).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
The number of threshold words on \(n\) letters grows exponentially for every \(n\geq 27\),
Journal of Integer Sequences 23(3), Article 20.3.1 (2020).
DOI
arXiv
 K. J. Balodis, M. E. Kroeker, L. Mol, and O. R. Oellermann,
On the mean order of connected induced subgraphs of block graphs, Australasian Journal of Combinatorics 76(1), 128148 (2020).
DOI
arXiv
 L. Mol, N. Rampersad, J. Shallit, and M. Stipulanti,
Cobham's theorem and automaticity, International Journal of Foundations of Computer Science 30(8), 13631379 (2019).
DOI
arXiv
 L. Mol and O. R. Oellermann,
Maximizing the mean subtree order, Journal of Graph Theory 91(4), 326352 (2019).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
Circular repetition thresholds on some small alphabets: Last cases of Gorbunova's Conjecture,
Electronic Journal of Combinatorics 26(2), #P2.31 (2019).
DOI
arXiv
 J. I. Brown, L. Mol, and O. R. Oellermann,
On the roots of Wiener polynomials of graphs,
Discrete Mathematics 341(9), 23982408 (2018).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
Avoidance bases for formulas with reversal,
Theoretical Computer Science 738, 2541 (2018).
DOI
arXiv
 M. E. Kroeker, L. Mol, and O. R. Oellermann,
On the mean connected induced subgraph order of cographs,
Australasian Journal of Combinatorics 71(1), 161183 (2018).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
On avoidability of formulas with reversal,
RAIRO  Theoretical Informatics and Applications 51, 181189 (2018).
DOI
arXiv
 J. I. Brown and L. Mol, The shape of node reliability,
Discrete Applied Mathematics 238, 4155 (2018).
DOI
arXiv
 J. D. Currie, L. Mol, and N. Rampersad,
A family of formulas with reversal of high avoidability index,
International Journal of Algebra and Computation 27(5), 477494 (2017).
DOI
arXiv
 J. I. Brown and L. Mol, On the roots of allterminal reliability polynomials,
Discrete Mathematics 320(6), 12871299 (2017).
DOI
arXiv
 J. I. Brown and L. Mol, On the roots of the node reliability polynomial,
Networks 68(3), 238246 (2016).
DOI
arXiv
Conference Proceedings
 J. D. Currie and L. Mol,
The undirected repetition threshold, WORDS 2019: Proceedings of the 12th International Conference on Words (LNCS 11682), 145158 (2019).
DOI
arXiv
Selected Talks
 Squarefree words: Theme and variations,
CBU Mathematics Seminar, Cape Breton University, June 2022.
Slides
 On connectivity of orientations of graphs,
CMS Summer Meeting 2022, Memorial University, June 2022.
Slides
 Squarefree words: Theme and variations,
TRU Mathematics Seminar, Thompson Rivers University, October 2021.
Slides
 The mean subtree order of graphs under edge addition,
Average Graph Parameters Minisymposium, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), online, May 2021.
Slides
 The threshold dimension of a graph,
CMS Winter Meeting, online, December 2020.
Slides
 Extremal squarefree words and variations,
One World Combinatorics on Words Seminar, online, June 2020.
Slides Video
 The repetition threshold for binary rich words,
AMS Special Session on Sequences, Words, and Automata,
Joint Mathematics Meetings, Denver, Colorado, January 2020.
Slides
 The repetition threshold for binary rich words,
Mathematics and Statistics Seminar,
University of Winnipeg, September 2019.
Slides
 The undirected repetition threshold,
Words 2019,
Loughborough University, September 2019.
Slides
 The threshold dimension of a graph,
East Coast Combinatorics Conference,
St. Francis Xavier University, August 2019.
Slides
 The mean subtree order and the mean connected induced subgraph order,
Average Graph Parameters Minisymposium,
Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Simon Fraser University, May 2019.
Slides
 The subtree polynomial,
Graph Polynomials Minisymposium,
Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Simon Fraser University, May 2019.
Slides
 The circular repetition threshold for small alphabets,
Prairie Discrete Math Workshop, Brandon University, June 2018.
Slides
 Circular repetition thresholds for small alphabets,
SIAM Conference on Discrete Mathematics, University of Colorado, Denver, June 2018.
Slides
 On the roots of Wiener polynomials of graphs,
Graph Polynomials Minisymposium,
SIAM Conference on Discrete Mathematics, University of Colorado, Denver, June 2018.
Slides
 Maximizing mean subtree order for classes of trees,
Average Graph Parameters Minisymposium,
Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Ryerson University, June 2017.
Slides
 Roots of allterminal reliability and node reliability polynomials,
Graph Polynomials Minisymposium,
Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Ryerson University, June 2017.
Slides
Theses
 On connectedness and graph polynomials, PhD Thesis, Dalhousie University, 2016.
Supervisor: Jason Brown. DalSpace
 On the uniformity space of hypergraphs, Master's Thesis, Dalhousie University, 2012.
Supervisor: Jason Brown. DalSpace