Transversal spaces

Victor Bryant and Hazel Perfect
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Victor Bryant: University of Sheffield, Department of Pure Mathematics
Hazel Perfect: University of Sheffield, Department of Pure Mathematics

Chapter Chapter Four in Independence Theory in Combinatorics, 1980, pp 65-99 from Springer

Abstract: Abstract Let A = (A1,…, A n ) be a family of subsets of a given set E. A subset {x1,…, xn}≠ of E such that xi ∈ Ai for each i (1≤ i≤ n) is called a transversal of A. Of course, not every family possesses a transversal. For example, the family $$(\{ a,b,c\} ,\{ d,e\} ,\{ a,c\} )$$ (where a, b, c, d, e are assumed distinct) has several transversals, one being {a, b, c, d}, with (for instance) a∈{a, b, c},b∈ {a, b}, d ∈ {d, e} and c∈{a,c}; whereas the family $$(\{ a,b\} ,\{ a,b\} ,\{ a\} )$$ has none. A partial transversal of A of length / is a transversal of a subfamily of/ sets of A So, for example, the latter family above has a partial transversal {a, b} of length 2, this being a transversal of ({a, b}, {a}).

Keywords: Bipartite Graph; Directed Graph; Hamiltonian Path; Disjoint Path; Initial Vertex (search for similar items in EconPapers)
Date: 1980
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DOI: 10.1007/978-94-009-5900-2_4

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