Lucas Mol

activity

20172025

most citedOn the Mean Connected Induced Subgraph Order of Cographs

8 citations · 12 across the 9 of their papers we have counts for

collaborators

Showing 2019Show all

5 papers · 1 filter

math.CO2019

The Weak Circular Repetition Threshold Over Large Alphabets

Lucas Mol, Narad Rampersad

The repetition threshold for words on $n$ letters, denoted $\mbox{RT}(n)$, is the infimum of the set of all $r$ such that there are arbitrarily long $r$ -free words over $n$ letters…

math.CO2019★ 1 cited

On the Mean Subtree Order of Graphs Under Edge Addition

Ben Cameron, Lucas Mol

For a graph $G$ , the mean subtree order of $G$ is the average order of a subtree of $G$ . In this note, we provide counterexamples to a recent conjecture of Chin, Gordon, MacPhee, a…

math.CO2019

The Number of Threshold Words on $n$ Letters Grows Exponentially for Every $n \geq 27$

James D. Currie, Lucas Mol, Narad Rampersad

For every $n \geq 27$ , we show that the number of $n / (n - 1)^{+}$ -free words (i.e., threshold words) of length $k$ on $n$ letters grows exponentially in $k$ . This settles all but finite…

math.CO2019

The maximum average connectivity among all orientations of a graph

Rocio M. Casablanca, Peter Dankelmann, Wayne Goddard +2

For distinct vertices $u$ and $v$ in a graph $G$ , the {\em connectivity} between $u$ and $v$ , denoted $κ_{G} (u, v)$ , is the maximum number of internally disjoint $u$ -- $v$ paths in $G$ …

math.CO2019

The undirected repetition threshold

James D. Currie, Lucas Mol

For rational $1 < r \leq 2$ , an undirected $r$ -power is a word of the form $x y x^{'}$ , where $x$ is nonempty, $x^{'} \in {x, x^{R}}$ , and $∣ x y x^{'} ∣/∣ x y ∣ = r$ . The undirected repetition thr…

The Weak Circular Repetition Threshold Over Large Alphabets

On the Mean Subtree Order of Graphs Under Edge Addition

The Number of Threshold Words on n Letters Grows Exponentially for Every n≥27

The maximum average connectivity among all orientations of a graph

The undirected repetition threshold

The Number of Threshold Words on $n$ Letters Grows Exponentially for Every $n \geq 27$