On computing quaternion quotient graphs for function fields

Gebhard Böckle; Ralf Butenuth

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This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in $O (| V | + | E |)$ time for any non-trivial class of graphs closed on graph minors. This applies in particular to planar graphs and graphs of bounded genus. Both algorithms run on a pointer machine and they require no a priori knowledge of the structure of the class except for its density. Edge weights are only compared.