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Exponential Families of Non-isomorphic Non-triangular Orientable Genus Embeddings of Complete Graphs

✍ Scribed by Vladimir P. Korzhik; Heinz-Jurgen Voss

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 421 KB
Volume: 86
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2122

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that for every i 2 f1; 2; . . . ; 11g=f3; 4; 7g the complete graph K 12sþi for s5dðiÞ 2 f1; 2; 3; 4g has at least hðiÞ4 s non-isomorphic orientable genus embeddings, where hðiÞ 2 1; 1 2 ; 1 4 ; 1 8

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We prove that the number of non-isomorphic face 2-colourable triangulations of the complete graph K n in an orientable surface is at least 2 n 2 Â54&O(n) for n congruent to 7 or 19 modulo 36, and is at least 2 2n 2 Â81&O(n) for n congruent to 19 or 55 modulo 108.