Planar embeddings with infinite faces

Craig Paul Bonnington, Mark E Watkins

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


We investigate vertex-transitive graphs that admit planar embeddings having infinite faces, i.e., faces whose boundary is a double ray. In the case of graphs with connectivity exactly 2, we present examples wherein no face is finite. In particular, the planar embeddings of the Cartesian product of the r-valent tree with K2 are comprehensively studied and enumerated, as are the automorphisms of the resulting maps, and it is shown for r A? 3 that no vertex-transitive group of graph automorphisms is extendable to a group of homeomorphisms of the plane. We present all known families of infinite, locally finite, vertex-transitive graphs of connectivity 3 and an infinite family of 4-connected graphs that admit planar embeddings wherein each vertex is incident with an infinite face.
Original languageEnglish
Pages (from-to)257 - 275
Number of pages19
JournalJournal of Graph Theory
Issue number4
Publication statusPublished - 2003
Externally publishedYes

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