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List-Compactness of Infinite Directed Graphs

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Abstract.

A digraph H is homomorphically compact if the digraphs G which admit homomorphisms to H are exactly the digraphs whose finite subdigraphs all admit homomorphisms to H. In this paper we define a similar notion of compactness for list-homomorphisms. We begin by showing that it is essentially only finite digraphs that are compact with respect to list-homomorphisms. We then explore the effects of restricting the types of list-assignments which are permitted, and obtain some richer characterizations.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada. e-mail: bauslaug@math.ucalgary.ca, , , , , , CA

    Bruce L. Bauslaugh

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  1. Bruce L. Bauslaugh
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Received: May 16, 1997 Final version received: January 16, 1998

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Bauslaugh, B. List-Compactness of Infinite Directed Graphs. Graphs Comb 17, 17–38 (2001). https://doi.org/10.1007/s003730170052

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  • DOI: https://doi.org/10.1007/s003730170052

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