# Lucas Mol

## Assistant Teaching Professor

### Department of Mathematics and Statistics, Thompson Rivers University

Home Research Teaching

## Research

### Preprints Submitted for Publication

1. A. Baranwal, J. D. Currie, L. Mol, P. Ochem, N. Rampersad, and J. Shallit, Antisquares and critical exponents, September 2022. arXiv
2. J. D. Currie, L. Mol, N. Rampersad, and J. Shallit, Extending Dekking's construction of an infinite binary word avoiding abelian 4-powers, November 2021. arXiv

### Publications

1. L. Mol, O. R. Oellermann, and V. Oswal, On average (edge-)connectivity of minimally k-(edge-)connected graphs, Bulletin of the ICA 94, 95-110 (2022). DOI arXiv
Supplemental Files: Sage Jupyter Notebook (.ipynb), Printout of Notebook (.pdf)
2. 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, 543-570 (2022). DOI arXiv
3. L. Mol and N. Rampersad, Lengths of extremal square-free words, Contributions to Discrete Mathematics 16(1), 8-19 (2021). DOI arXiv
Supplemental Files: Short Extremal Square-Free Words, Short Extremal Square-Free Circular Words
4. J. D. Currie and L. Mol, The undirected repetition threshold and undirected pattern avoidance, Theoretical Computer Science 866, 56-69 (2021). DOI arXiv
5. 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
6. B. Cameron and L. Mol, On the mean subtree order of graphs under edge addition, Journal of Graph Theory, online ready, 2021. DOI arXiv
7. R. M. Casablanca, L. Mol, and O. R. Oellermann, Average connectivity of minimally 2-connected graphs and average edge-connectivity of minimally 2-edge-connected graphs, Discrete Applied Mathematics 289, 233-247 (2021). DOI arXiv
8. J. I. Brown, C. J. Colbourn, D. Cox, C. Graves, and L. Mol, Network reliability: Heading out on the highway, Networks 77(1), 146-160 (2021). DOI
9. L. Mol, N. Rampersad, and J. Shallit, Extremal overlap-free and extremal $$\beta$$-free binary words, Electronic Journal of Combinatorics 27(4), Article P4.42 (2020). DOI arXiv
10. L. Mol and N. Rampersad, The weak circular repetition threshold over large alphabets, RAIRO - Theoretical Informatics and Applications 54, Article 6, 2020. DOI arXiv
11. L. Mol, M. J. H. Murphy, and O. R. Oellermann, The threshold dimension of a graph, Discrete Applied Mathematics 287, 118-133 (2020). DOI arXiv
12. J. I. Brown and L. Mol, On the roots of the subtree polynomial, European Journal of Combinatorics 89, (2020). DOI arXiv
13. 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
14. 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
15. 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), 128-148 (2020). DOI arXiv
16. L. Mol, N. Rampersad, J. Shallit, and M. Stipulanti, Cobham's theorem and automaticity, International Journal of Foundations of Computer Science 30(8), 1363-1379 (2019). DOI arXiv
17. L. Mol and O. R. Oellermann, Maximizing the mean subtree order, Journal of Graph Theory 91(4), 326-352 (2019). DOI arXiv
18. 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
19. J. I. Brown, L. Mol, and O. R. Oellermann, On the roots of Wiener polynomials of graphs, Discrete Mathematics 341(9), 2398-2408 (2018). DOI arXiv
20. J. D. Currie, L. Mol, and N. Rampersad, Avoidance bases for formulas with reversal, Theoretical Computer Science 738, 25-41 (2018). DOI arXiv
21. M. E. Kroeker, L. Mol, and O. R. Oellermann, On the mean connected induced subgraph order of cographs, Australasian Journal of Combinatorics 71(1), 161-183 (2018). DOI arXiv
22. J. D. Currie, L. Mol, and N. Rampersad, On avoidability of formulas with reversal, RAIRO - Theoretical Informatics and Applications 51, 181-189 (2018). DOI arXiv
23. J. I. Brown and L. Mol, The shape of node reliability, Discrete Applied Mathematics 238, 41-55 (2018). DOI arXiv
24. 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), 477-494 (2017). DOI arXiv
25. J. I. Brown and L. Mol, On the roots of all-terminal reliability polynomials, Discrete Mathematics 320(6), 1287-1299 (2017). DOI arXiv
26. J. I. Brown and L. Mol, On the roots of the node reliability polynomial, Networks 68(3), 238-246 (2016). DOI arXiv

### Conference Proceedings

1. J. D. Currie and L. Mol, The undirected repetition threshold, WORDS 2019: Proceedings of the 12th International Conference on Words (LNCS 11682), 145-158 (2019). DOI arXiv

### Selected Talks

1. Square-free words: Theme and variations, CBU Mathematics Seminar, Cape Breton University, June 2022. Slides
2. On connectivity of orientations of graphs, CMS Summer Meeting 2022, Memorial University, June 2022. Slides
3. Square-free words: Theme and variations, TRU Mathematics Seminar, Thompson Rivers University, October 2021. Slides
4. The mean subtree order of graphs under edge addition, Average Graph Parameters Minisymposium, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), online, May 2021. Slides
5. The threshold dimension of a graph, CMS Winter Meeting, online, December 2020. Slides
6. Extremal square-free words and variations, One World Combinatorics on Words Seminar, online, June 2020. Slides Video
7. The repetition threshold for binary rich words, AMS Special Session on Sequences, Words, and Automata, Joint Mathematics Meetings, Denver, Colorado, January 2020. Slides
8. The repetition threshold for binary rich words, Mathematics and Statistics Seminar, University of Winnipeg, September 2019. Slides
9. The undirected repetition threshold, Words 2019, Loughborough University, September 2019. Slides
10. The threshold dimension of a graph, East Coast Combinatorics Conference, St. Francis Xavier University, August 2019. Slides
11. 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
12. The subtree polynomial, Graph Polynomials Minisymposium, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Simon Fraser University, May 2019. Slides
13. The circular repetition threshold for small alphabets, Prairie Discrete Math Workshop, Brandon University, June 2018. Slides
14. Circular repetition thresholds for small alphabets, SIAM Conference on Discrete Mathematics, University of Colorado, Denver, June 2018. Slides
15. On the roots of Wiener polynomials of graphs, Graph Polynomials Minisymposium, SIAM Conference on Discrete Mathematics, University of Colorado, Denver, June 2018. Slides
16. Maximizing mean subtree order for classes of trees, Average Graph Parameters Minisymposium, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Ryerson University, June 2017. Slides
17. Roots of all-terminal reliability and node reliability polynomials, Graph Polynomials Minisymposium, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Ryerson University, June 2017. Slides

### Theses

1. On connectedness and graph polynomials, PhD Thesis, Dalhousie University, 2016.
Supervisor: Jason Brown. DalSpace
2. On the uniformity space of hypergraphs, Master's Thesis, Dalhousie University, 2012.
Supervisor: Jason Brown. DalSpace