Randy Davila

collaborators

4 papers

math.CO2026

The Havel--Hakimi Residue of Common-Divisor Graphs: Resolving and Extending a Problem of Graffiti and Erdős

Randy Davila

For an integer $n \geq 2$ , let $G_{n}$ be the graph on ${2, \dots, n}$ in which distinct integers are adjacent when they have a nontrivial common divisor. Conjecture 448 of Fajtlowicz…

math.CO2026

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 $I^\pm_{F} (G)$ as the maximum order of any induced subgraph of $G$ that belongs to the family $F$ .…

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

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…

The Havel--Hakimi Residue of Common-Divisor Graphs: Resolving and Extending a Problem of Graffiti and Erdős

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

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

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

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