Self-dual orientable embeddings of Kn
نویسندگان
چکیده
منابع مشابه
Regular Hamiltonian embeddings of the complete bipartite graph Kn,n in an orientable surface
An embedding M of a graph G is said to be regular if and only if for every two triples (v1, e1, f1) and (v2, e2, f2), where ei is an edge incident with the vertex vi and the face fi, there exists an automorphism of M which maps v1 to v2, e1 to e2 and f1 to f2. We show that for n 6≡ 0 (mod 8) there is, up to isomorphism, precisely one regular Hamiltonian embedding of Kn,n in an orientable surfac...
متن کاملRegular hamiltonian embeddings of Kn, n and regular triangular embeddings of Kn, n, n
We give a group-theoretic proof of the following fact, proved initially by methods of topological design theory: Up to isomorphism, the number of regular hamiltonian embeddings of Kn,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of Kn,n,n. This is a preprint of an article accepted fo...
متن کاملPolyhedral Embeddings of Snarks in Orientable Surfaces
An embedding of a 3-regular graph in a surface is called polyhedral if its dual is a simple graph. An old graph-coloring conjecture is that every 3-regular graph with a polyhedral embedding in an orientable surface has a 3-edge-coloring. An affirmative solution of this problem would generalize the dual form of the Four Color Theorem to every orientable surface. In this paper we present a negati...
متن کاملFano Plane’s Embeddings on Compact Orientable Surfaces
In this paper we study embeddings of the Fano plane as a bipartite graph. We classify all possible embeddings especially focusing on those with non-trivial automorphism group. We study them in terms of rotation systems, isomorphism classes and chirality. We construct quotients and show how to obtain information about face structure and genus of the covering embedding. As a by-product of the cla...
متن کاملOrientable embeddings and orientable cycle double covers of projective-planar graphs
In a closed 2-cell embedding of a graph each face is homeomorphic to an open disk and is bounded by a cycle in the graph. The Orientable Strong Embedding Conjecture says that every 2-connected graph has a closed 2-cell embedding in some orientable surface. This implies both the Cycle Double Cover Conjecture and the Strong Embedding Conjecture. In this paper we prove that every 2-connected proje...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1975
ISSN: 0095-8956
DOI: 10.1016/0095-8956(75)90063-5