Abstract
An infinite self-complementary (s.c.) graph is quasi-locally-finite if, for each vertex ξ, either the number of vertices adjacent to ξ is finite or the number of vertices not adjacent to ξ is finite. We prove that every quasi-locally-finite s.c. graph has a spanning subgraph consisting of two 1-way infinite arcs, and give an example of a countable s.c. graph (not quasi-locally-finite) which requires infinitely many 1-way infinite arcs for a spanning subgraph.
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