10 citations · 12 across the 8 of their papers we have counts for
12 papers
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…
Independence, induced subgraphs, and domination in -free graphs
Yair Caro, Randy Davila, Michael A. Henning +1
Let be a graph and a family of graphs. Define as the maximum order of any induced subgraph of that belongs to the family . F…
Comparing the -independence number of regular graphs to the -independence number of their line graphs
Yair Caro, Randy Davila, Ryan Pepper
Let be a simple graph and let denote the \emph{line graph} of . A \emph{-independent} set in is a set of vertices such that the subgraph ind…
Conjecture of TxGraffiti: Independence, domination, and matchings
Yair Caro, Randy Davila, Michael Henning +1
TxGraffiti is an automated conjecturing program that produces graph theoretic conjectures in the form of conjectured inequalities. This program written and maintained by the second…
New results relating independence and matchings
Yair Caro, Randy Davila, Ryan Pepper
In this paper we study relationships between the \emph{matching number}, written , and the \emph{independence number}, written . Our first main result is to show \[ α(G…
Maximum oriented forcing number for complete graphs
Yair Caro, Ryan Pepper
The maximum oriented -forcing number of a simple graph , written $\MOF_k(G)$, is the maximum directed -forcing number among all orientations of . This invariant was rec…