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How to determine the maximum genus of a graph

✍ Scribed by Nguyen Huy Xuong

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
477 KB
Volume
26
Category
Article
ISSN
0095-8956

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## Abstract Some of the early questions concerning the maximum genus of a graph have now been answered. In this paper we survey the progress made on such problems and present some recent results, outlining proofs for some of the major theorems.

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Skoviera, M., The maximum genus of graphs of diameter two, Discrete Mathematics 87 (1991) 175-180. Let G be a (finite) graph of diameter two. We prove that if G is loopless then it is upper embeddable, i.e. the maximum genus y,&G) equals [fi(G)/Z], where /3(G) = IF(G)1 -IV(G)1 + 1 is the Betti numbe