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A Characterization of Mixed Branching Greedoids
Steven J. Tedford
Department of Mathematical Sciences, Franklin and Marshall College, Lancaster, PA 17604-3003, USA
steven.tedford@fandm.edu
Annals of Combinatorics 11 (1) p.79-100 March, 2007
AMS Subject Classification: 05B99, 05C99
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}; {Ø; {a}; {b}; {c}; {a; b}; {a; c}; {b; c}})

as a minor.

Keywords: greedoid, forbidden minor, rooted mixed graph

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