3-connected planar spaces uniquely embed in the sphere
نویسندگان
چکیده
منابع مشابه
3-connected Planar Spaces Uniquely Embed in the Sphere
We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere — i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if Ḡ is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in Ḡ, then Ḡ has a...
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A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G−e is not a uniquely k-colorable graph for any edge e ∈ E(G). In this paper, we prove that if G is an edge-critical uniquely 3-colorable planar graph, then |E(G)| 6 83 |V (G)| − 17 3 . On the other hand, there exis...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-03052-0