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On a Duality Principle in Infinite Bipartite Graphs
Author(s) -
Aharoni Ron
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-28.3.385
Subject(s) - bipartite graph , mathematics , conjecture , equivalence (formal languages) , combinatorics , duality (order theory) , discrete mathematics , extension (predicate logic) , robertson–seymour theorem , graph , 1 planar graph , line graph , computer science , programming language
We consider an extension of König's duality theorem to infinite bipartite graphs, conjectured by Erdös. We prove an equivalence between this conjecture and another conjecture, and using the equivalence we prove it in certain cases.