Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Davila Randy"'
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 42, Iss 3, Pp 921-935 (2022)
In this paper we study relationships between the matching number, written µ(G), and the independence number, written α(G). Our first main result is to show
Externí odkaz:
https://doaj.org/article/43f47dc1c919410a8252c54bfaed9cd6
We prove that the \emph{standard zero forcing number} $Z(G)$ and the \emph{positive semidefinite zero forcing number} $Z_+(G)$ are equal for all claw-free graphs $G$. This result resolves a conjecture proposed by the computer program \emph{TxGraffiti
Externí odkaz:
http://arxiv.org/abs/2412.03463
Autor:
Davila, Randy
This paper introduces the \emph{Optimist}, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the \emph{Optimist} generates conjectures that bot
Externí odkaz:
http://arxiv.org/abs/2411.09158
Autor:
Davila, Randy
\emph{TxGraffiti} is a data-driven, heuristic-based computer program developed to automate the process of generating conjectures across various mathematical domains. Since its creation in 2017, \emph{TxGraffiti} has contributed to numerous mathematic
Externí odkaz:
http://arxiv.org/abs/2409.19379
Let $G$ be a simple graph, and let $p$, $q$, and $r$ be non-negative integers. A \emph{$p$-independent} set in $G$ is a set of vertices $S \subseteq V(G)$ such that the subgraph induced by $S$ has maximum degree at most $p$. The \emph{$p$-independenc
Externí odkaz:
http://arxiv.org/abs/2409.03233
Autor:
Davila, Randy
Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using convolutional neural
Externí odkaz:
http://arxiv.org/abs/2407.07827
Autor:
Davila, Randy
\emph{TxGraffiti} is a machine learning and heuristic based artificial intelligence designed to automate the task of conjecturing in mathematics. Since its inception, TxGraffiti has generated many surprising conjectures leading to publication in resp
Externí odkaz:
http://arxiv.org/abs/2407.02731
Autor:
Davila Randy, Henning Michael A.
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 40, Iss 3, Pp 733-754 (2020)
A dynamic coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non
Externí odkaz:
https://doaj.org/article/68b6aec13c7e4c08ac834e26eb7beec0
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 40, Iss 1, Pp 209-225 (2020)
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show t
Externí odkaz:
https://doaj.org/article/3ac0f954be5143ae9a02343465558ff4
Autor:
Davila, Randy R.
This paper proves a conjecture generated by the artificial intelligence conjecturing program called \emph{TxGraffiti}. More specifically, we show that if $G$ is a connected, cubic, and claw-free graph, then $Z(G) \le \gamma(G) + 2$, where $Z(G)$ and
Externí odkaz:
http://arxiv.org/abs/2406.19231