Face Covers and the Genus of Apex Graphs

نویسنده

  • Bojan Mohar
چکیده

A graph G is an apex graph if it contains a vertex w such that G w is a planar graph It is easy to see that the genus g G of the apex graph G is bounded above by where is the minimum face cover of the neighbors of w taken over all planar embeddings of G w The main result of this paper is the linear lower bound g G if G w is connected and It is also proved that computing the genus of apex graphs is NP hard

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تاریخ انتشار 2007