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A note on immersion intertwines of infinite graphs
Author(s) -
Barnes Matthew,
Oporowski Bogdan
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22440
Subject(s) - antichain , mathematics , immersion (mathematics) , combinatorics , discrete mathematics , graph , cograph , line graph , pathwidth , partially ordered set , pure mathematics
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.