Attila Joó
Abstract
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We prove that if M and N are finitary matroids on a common countable edge set E then they admit a common independent set I such that there is a bipartition E=EM∪EN for which I∩EM spans EM in M and I∩EN spans EN in N. It answers positively the Matroid Intersection Conjecture of Nash-Williams in the countable case.
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We prove that if M and N are finitary matroids on a common countable edge set E then they admit a common independent set I such that there is a bipartition E=EM∪EN for which I∩EM spans EM in M and I∩EN spans EN in N. It answers positively the Matroid Intersection Conjecture of Nash-Williams in the countable case.
Key concepts: Finitary, Countable set, Matroid, Combinatorics, Mathematics, Conjecture, Intersection (aeronautics), Discrete mathematics