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The Membership Problem in Jump Systems

✍ Scribed by László Lovász

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
384 KB
Volume
70
Category
Article
ISSN
0095-8956

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✦ Synopsis

dedicated to professor w. t. tutte on the occasion of his eightieth birthday

A jump system is a set of lattice points satisfying a certain exchange axiom. This notion was introduced by Bouchet and Cunningham [2], as a common generalization of (among others) the sets of bases of a matroid and degree sequences of subgraphs of a graph. We prove, under additional assumptions, a min-max formula for the distance of a lattice point from a jump system. The conditions are met in the examples above, and so our formula contains, as special cases, Tutte's f-factortheorem and Edmonds' matroid intersection theorem.

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