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Unavoidable set of face types for planar maps

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The type of a face f of a planar map is a sequence of degrees of vertices of f as they are encountered when traversing the boundary of f. A set 𝒯 of face types is found such that in any normal planar map there is a face with type from 𝒯. The set 𝒯 has four infinite series of types as, in a certain sense, the minimum possible number. An analogous result is applied to obtain new upper bounds for the cyclic chromatic number of 3-connected planar maps.
Opis fizyczny
  • Department of Geometry and Algebra, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
  • Department of Geometry and Algebra, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
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