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This article introduces a special issue of Philosophical Investigations focused on Ludwig Wittgenstein's philosophy of mathematics and its connection to the philosophy of mathematical practice (PMP). The author acknowledges that while Wittgenstein is a highly influential philosopher, his work in the philosophy of mathematics is often overshadowed by his other writings. The special issue includes nine articles that cover various topics related to Wittgenstein's philosophy of mathematics and PMP. The articles explore Wittgenstein's practice-based approach to meaning, his views on set theory, his struggles with arithmetic and higher mathematics, and his critique of Cantorian set theory. The volume aims to deepen our understanding of mathematical practice, contribute to the discourse on Wittgenstein's philosophy of mathematics, and introduce Wittgensteinian ideas to the wider community of philosophers of mathematical practice. [Extracted from the article]

In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finite infinite graphs. For this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. In this paper we focus on conditions involving claws, nets and bulls as induced subgraphs. We extend Hamiltonicity results for finite claw‐free and net‐free graphs by Shepherd to locally finite graphs. Moreover, we generalise a classification of finite claw‐free and net‐free graphs by Shepherd to locally finite ones. Finally, we extend to locally finite graphs a Hamilto)nicity result by Ryjáček involving a relaxed condition of being bull‐free. [ABSTRACT FROM AUTHOR]