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arXiv · 2401.14768

On Mixed Cages of Girth 6

Gabriela Araujo-Pardo·Mirabel Mendoza-Cadena
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Abstract

A [z,r;g]-mixed cage is a mixed graph of minimum order such that each vertex has z in-arcs, z out-arcs, r edges, and it has girth g. We present an infinite family of mixed graphs with girth 6. This construction also provides an upper bound on the minimum order of mixed cages of girth 6. Additionally,we introduce a lower bound on the minimum order for any mixed cage.

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Gabriela Araujo-Pardo, Mirabel Mendoza-Cadena. 2026-02-03. On Mixed Cages of Girth 6. https://arxiv.org/abs/2401.14768

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