Stars and bunches in planar graphs. Part I: Triangulations

O.V. Borodin, Haitze J. Broersma, A. Glebov, J. van den Heuvel

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Given a plane graph, a $k$-star at $u$ is a set of $k$ vertices with a common neighbour $u$; and a bunch is a maximal collection of paths of length at most two in the graph, such that all paths have the same end vertices and the edges of the paths form consecutive edges (\,in the natural order in the plane graph\,) around the two end vertices. We prove a theorem on the structure of plane triangulations in terms of stars and bunches. The result states that a plane triangulation contains a $(d-1)$-star centred at a vertex of degree $d\leq5$ and the sum of the degrees of the vertices in the star is bounded, or there exists a large bunch.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages18
ISBN (Print)0169-2690
Publication statusPublished - 2002

Publication series

NameMemorandum Faculteit TW
PublisherDepartment of Applied Mathematics, University of Twente
ISSN (Print)0169-2690


  • EWI-3452
  • MSC-05C12
  • MSC-05C15
  • IR-65819
  • METIS-208266

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