Deciding soccer scores and partial orientations of graphs.

Pálvölgyi, Dömötör

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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.

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Helly Property for Subtrees

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We prove, following [5, p. 92], that any family of subtrees of a finite tree satisfies the Helly property.MML identifier: HELLY, version: 7.8.09 4.97.1001