Nonorientable hamilton cycle embeddings of complete tripartite graphs
نویسندگان
چکیده
منابع مشابه
Nonorientable hamilton cycle embeddings of complete tripartite graphs
A cyclic construction is presented for building embeddings of the complete tripartite graph Kn,n,n on a nonorientable surface such that the boundary of every face is a hamilton cycle. This construction works for several families of values of n, and we extend the result to all n with some methods of Bouchet and others. The nonorientable genus of Kt,n,n,n, for t ≥ 2n, is then determined using the...
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In 1976, Stahl and White conjectured that the nonorientable genus of Kl,m,n, where l ≥ m ≥ n, is (l−2)(m+n−2) 2 . The authors recently showed that the graphs K3,3,3 , K4,4,1, and K4,4,3 are counterexamples to this conjecture. Here we prove that apart from these three exceptions, the conjecture is true. In the course of the paper we introduce a construction called a transition graph, which is cl...
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In an earlier paper the authors constructed a hamilton cycle embedding of Kn,n,n in a nonorientable surface for all n ≥ 1 and then used these embeddings to determine the genus of some large families of graphs. In this two-part series, we extend those results to orientable surfaces for all n 6= 2. In part II, a voltage graph construction is presented for building embeddings of the complete tripa...
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A 2-cell embedding of a graph G into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs Kn,n into nonorientable surfaces. Such a regular embedding of Kn,n exists only when n = 2p a1 1 p a2 2 · · · p ak k (a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.02.012