incoherent 发表于 2025-3-21 16:45:41

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EWER 发表于 2025-3-21 21:47:34

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顽固 发表于 2025-3-22 00:37:06

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Amnesty 发表于 2025-3-22 07:58:52

Graph Theory,Proper formulation of the map Color Problem and the Thread Problem and their solution requires some graph theoretical preparations.

Obliterate 发表于 2025-3-22 09:06:19

Classification of Surfaces,In this chapter we will present material that is well known; however we need not only the results, but also parts of the proofs as we shall see in later chapters. For more details of this theory see H. Seifert and Threlfall or M. Fréchet and Ky Fan .

解开 发表于 2025-3-22 13:16:23

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迎合 发表于 2025-3-22 17:02:30

Orientable Cases 1, 4, and 9,Now we will construct a triangular embedding of .. into an orientable surface for each . of the form .= 12.+ 4.

irreparable 发表于 2025-3-22 21:24:24

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出来 发表于 2025-3-23 02:54:06

Non-Orientable Cases (Index 1),It is our intention to determine the non-orientable genus of .. which means to prove formula (4.19). For . ≦ 8 this was already done in Sections 4.6 and 5.1.

epidermis 发表于 2025-3-23 07:03:55

Solutions of Index 2 and 3,Each of the current graphs we used in the previous chapters has the property that the given rotation induces . single circuit. The log of the circuit provides row 0 and all the other rows are determined by the additive rule (or for the extra rows (as row ., etc.) by Rule .*). We say row 0 . the whole scheme and the solution is of . 1.
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查看完整版本: Titlebook: Map Color Theorem; Gerhard Ringel Book 1974 Springer-Verlag Berlin Heidelberg 1974 Mehrfarbenproblem.boundary element method.form.proof.th