L. Kovacs, Hanna Lachnitt, S. Szeider:

"Formalizing Graph Trail Properties in Isabelle/HOL";

Talk: International Conference on Intelligent Computer Mathematics (CICM), Bertinoro, Forli, Italy; 2020-07-26 - 2020-07-31; in: "CICM 2020: Intelligent Computer Mathematics", LNCS, 12236 (2020), ISBN: 978-3-030-53518-6; 190 - 205.

We describe a dataset expressing and proving properties of graph trails, using Isabelle/HOL. We formalize the reasoning about strictly increasing and decreasing trails, using weights over edges, and prove lower bounds over the length of trails in weighted graphs. We do so by extending the graph theory library of Isabelle/HOL with an algorithm computing the length of a longest strictly decreasing graph trail starting from a vertex for a given weight distribution, and prove that any decreasing trail is also an increasing one.

http://dx.doi.org/10.1007/978-3-030-53518-6_12

https://publik.tuwien.ac.at/files/publik_292351.pdf

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