Face Covers and the Genus of Apex Graphs
نویسنده
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
منابع مشابه
Face Covers and the Genus Problem for Apex Graphs
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 τ − 1, where τ 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) ≥ τ/160 (if G − w is 3-connected and τ > 1). It is also proved th...
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