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- W4295698777 abstract "In this paper, we showcase the process of using an automated conjecturing program called emph{TxGraffiti} written and maintained by the second author. We begin by proving a conjecture formulated by emph{TxGraffiti} that for a claw-free graph $G$, the vertex cover number $beta(G)$ is greater than or equal to the zero forcing number $Z(G)$. Our proof of this result is constructive, and yields a polynomial time algorithm to find a zero forcing set with cardinality $beta(G)$. We also use the output of emph{TxGraffiti} to construct several infinite families of claw-free graphs for which $Z(G)=beta(G)$. Additionally, inspired by the aforementioned conjecture of emph{TxGraffiti}, we also prove a more general relation between the zero forcing number and the vertex cover number for any connected graph with maximum degree $Delta ge 3$, namely that $Z(G)leq (Delta-2)beta(G)$+1." @default.
- W4295698777 created "2022-09-14" @default.
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- W4295698777 date "2022-09-09" @default.
- W4295698777 modified "2023-09-28" @default.
- W4295698777 title "Computer assisted discovery: Zero forcing vs vertex cover" @default.
- W4295698777 doi "https://doi.org/10.48550/arxiv.2209.04552" @default.
- W4295698777 hasPublicationYear "2022" @default.
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