Randy Davila

activity

20242026

collaborators

5 papers

math.CO2026

Havel--Hakimi Residues of Common-Divisor Graphs: Complete Asymptotics and Prime-Counting Structure

Randy Davila

Let $G_{n}$ be the graph on ${2, \dots, n}$ in which two integers are adjacent when they have a common divisor greater than one. We determine the complete asymptotic expansion of it…

cs.DM2025

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator

Randy Davila, Boris Brimkov, Ryan Pepper

We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariant…

math.CO2025

Independence, induced subgraphs, and domination in $K_{1, r}$ -free graphs

Yair Caro, Randy Davila, Michael A. Henning +1

Let $G$ be a graph and $F$ a family of graphs. Define $α_{F} (G)$ as the maximum order of any induced subgraph of $G$ that belongs to the family $F$ . F…

math.CO2024

Comparing the $p$ -independence number of regular graphs to the $q$ -independence number of their line graphs

Yair Caro, Randy Davila, Ryan Pepper

Let $G$ be a simple graph and let $L (G)$ denote the \emph{line graph} of $G$ . A \emph{ $p$ -independent} set in $G$ is a set of vertices $S \subseteq V (G)$ such that the subgraph ind…

math.CO2024

Lower bounds for the total (distance) $k$ -domination number of a graph

Randy Davila

For $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total (distance) $k$ -dominating set} of $G$ is a set of vertices $S \subseteq V (G)$ such that every vertex in $G$ …

Havel--Hakimi Residues of Common-Divisor Graphs: Complete Asymptotics and Prime-Counting Structure

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator

Independence, induced subgraphs, and domination in K1,r​-free graphs

Comparing the p-independence number of regular graphs to the q-independence number of their line graphs

Lower bounds for the total (distance) k-domination number of a graph

Independence, induced subgraphs, and domination in $K_{1, r}$ -free graphs

Comparing the $p$ -independence number of regular graphs to the $q$ -independence number of their line graphs

Lower bounds for the total (distance) $k$ -domination number of a graph