Face Size and the Maximum Genus of a Graph 1. Simple Graphs1
Journal of Combinatorial Theory, Series B 80(2000)356-370 ，-0001，（）：
This paper shows that a simple graph which can be cellularly embedded on some closed surface in such a way that the size of each face does not exceed 7 is upper embeddable. This settles one of two conjectures posed by Nedela and S8 koviera (1990, in "Topics in Combinatorics and Graph Theory," pp. 519-529, Physica Verlag, Heidelberg). The other conjecture will be proved in a sequel to this paper.
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