Abstract
We consider several variations of the following problem: fix a countable graph G. Is an input graph H a(n induced) subgraph of G? If yes, can we find a copy of H in G? The challenge to classify the Weihrauch degrees of such problems was put forth recently by BeMent, Hirst, and Wallace (“Reverse mathematics and Weihrauch analysis motivated by finite complexity theory”, Computability, 2021). We report some initial results here, and in particular, solve one of their open questions.
Cipriani’s research was partially supported by the Italian PRIN 2017 Grant “Mathematical Logic: models, sets, computability”. He thanks Alberto Marcone and Manlio Valenti for useful discussions about the topics of this paper.
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Notes
- 1.
The proof that the sets are indeed \(\varPi ^0_5\) was provided to us by a referee.
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Cipriani, V., Pauly, A. (2023). The Complexity of Finding Supergraphs. In: Della Vedova, G., Dundua, B., Lempp, S., Manea, F. (eds) Unity of Logic and Computation. CiE 2023. Lecture Notes in Computer Science, vol 13967. Springer, Cham. https://doi.org/10.1007/978-3-031-36978-0_15
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