Metric properties of incomparability graphs with an emphasis on paths
DOI:
https://doi.org/10.55016/ojs/cdm.v17i1.73727Abstract
We describe some metric properties of incomparability graphs. We consider the problem of the existence of infinite paths, either induced or isometric, in the incomparability graph of a poset. Among other things, we show that if the incomparability graph of a poset is connected and has infinite diameter, then it contains an infinite induced path. Furthermore, if the diameter of the set of vertices of degree at least $3$ is infinite, then the graph contains as an induced subgraph either a comb or a kite.
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Copyright (c) 2022 Maurice Pouzet, Imed Zaguia
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