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- W2952220912 abstract "We call a bipartite graph {it homogeneous} if every finite partial automorphism which respects left and right can be extended to a total automorphism. A $(kappa,{lambda} )$ bipartite graph is a bipartite graph with left side of size $kappa$ and right side of size ${lambda}$. We show, using a theorem of Hrushovski on finite graphs, that there is a homogeneous $({aleph_0},2^{aleph_0} )$ bipartite graph of girth 4 (thus answering negatively a question by Kupitz and Perles), and that depending on the underlying set theory all homogeneous $({aleph_0},aleph_1)$ bipartite graphs may be isomorphic, or there may be $2^{aleph_1}$ many isomorphism types of $(aleph_0,aleph_1)$ homogeneous graphs." @default.
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- W2952220912 date "1994-09-06" @default.
- W2952220912 modified "2023-09-27" @default.
- W2952220912 title "Infinite homogeneous bipartite graphs with unequal sides" @default.
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