Publications (13)
Dynamic approach to k-forcing
Yair Caro, Ryan Pepper
The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this…
Proposal for a micromagnetic standard problem for materials with Dzyaloshinskii-Moriya interaction
David Cortés-Ortuño, Marijan Beg, Vanessa Nehruji +10
Understanding the role of the Dzyaloshinskii-Moriya interaction (DMI) for the formation of helimagnetic order, as well as the emergence of skyrmions in magnetic systems that lack i…
Degree Sequence Index Strategy
Yair Caro, Ryan Pepper
We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by which to bound graph invariants by certain indices in the ordered degree sequence. As an illustration…
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…
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 \[ Î…
Upper bounds on the k-forcing number of a graph
David Amos, Yair Caro, Randy Davila +1
Given a simple undirected graph and a positive integer , the -forcing number of , denoted , is the minimum number of vertices that need to be initially colored…
Bounds on the connected forcing number of a graph
Randy Davila, Michael Henning, Colton Magnant +1
In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph.…
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…
Extremal -forcing sets in oriented graphs
Yair Caro, Randy Davila, Ryan Pepper
This article studies the \emph{-forcing number} for oriented graphs, generalizing both the \emph{zero forcing number} for directed graphs and the -forcing number for simple g…
Regular independent sets
Yair Caro, Adriana Hansberg, Ryan Pepper
The regular independence number, introduced by Albertson and Boutin in 1990, is the size of a largest set of independent vertices with the same degree. Lower bounds were proven for…
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…
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 .…