A note on immersion intertwines of infinite graphs. Issue 1 (12th December 2018)

• Record Type: Journal Article
• Authors: Barnes, Matthew; Oporowski, Bogdan
• Is Part Of: Journal of graph theory. Volume 92:Issue 1(2019)
• Page Start: 57
• Page End: 62
• Publication Date: 2018-12-12
• Subjects: 05C15; graph -- immersion -- intertwine; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22440
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: We present a construction of two infinite graphs G 1 and G 2, and of an infinite set F of graphs such that F is an antichain with respect to the immersion relation and, for each graph G in F, both G 1 and G 2 are subgraphs of G, but no graph properly immersed in G admits an immersion of G 1 and of G 2 . This shows that the class of infinite graphs ordered by the immersion relation does not have the finite intertwine property.