Two linear time algorithms for MST on minor closed graph classes

Martin Mareš

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Let $Λ$ be a maximal $𝔽_{q} [T]$ -order in a division quaternion algebra over $𝔽_{q} (T)$ which is split at the place $\infty$ . The present article gives an algorithm to compute a fundamental domain for the action of the group of units $Λ^{*}$ on the Bruhat-Tits tree $𝒯$ associated to ${PGL}_{2} (𝔽_{q} ((1 / T)))$ . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group $Λ^{*}$ in terms of generators and relations. Moreover we determine an...