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A Characterization of Mixed Branching Greedoids

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Abstract.

Branching greedoids have been defined and characterized for both directed and undirected rooted graphs. Such greedoids can be extended to rooted mixed graphs – graphs with both directed and undirected edges. These greedoids are characterized by a list of forbidden minors.

If Ω is a rooted mixed graph, its mixed branching greedoid has the edges of Ω as its ground set and the collection of arborescences as its feasible sets. The set of mixed branching greedoids is exactly the set of local forest greedoids without

$$(\{a, b, c\}, \{\emptyset, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}\})$$

as a minor.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Franklin and Marshall College, Lancaster, PA, 17604-3003, USA

    Steven J. Tedford

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  1. Steven J. Tedford
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Correspondence to Steven J. Tedford.

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Received July 12, 2005

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Tedford, S.J. A Characterization of Mixed Branching Greedoids. Ann. Comb. 11, 79–100 (2007). https://doi.org/10.1007/s00026-007-0307-0

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  • DOI: https://doi.org/10.1007/s00026-007-0307-0

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