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Titlebook: Map Color Theorem; Gerhard Ringel Book 1974 Springer-Verlag Berlin Heidelberg 1974 Mehrfarbenproblem.boundary element method.form.proof.th

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书目名称Map Color Theorem
编辑Gerhard Ringel
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Map Color Theorem;  Gerhard Ringel Book 1974 Springer-Verlag Berlin Heidelberg 1974 Mehrfarbenproblem.boundary element method.form.proof.th
描述In 1890 P. J. Heawood [35] published a formula which he called the Map Colour Theorem. But he forgot to prove it. Therefore the world of mathematicians called it the Heawood Conjecture. In 1968 the formula was proven and therefore again called the Map Color Theorem. (This book is written in California, thus in American English. ) Beautiful combinatorial methods were developed in order to prove the formula. The proof is divided into twelve cases. In 1966 there were three of them still unsolved. In the academic year 1967/68 J. W. T. Youngs on those three cases at Santa Cruz. Sur­ invited me to work with him prisingly our joint effort led to the solution of all three cases. It was a year of hard work but great pleasure. Working together was extremely profitable and enjoyable. In spite of the fact that we saw each other every day, Ted wrote a letter to me, which I present here in shortened form: Santa Cruz, March 1, 1968 Dear Gerhard: Last night while I was checking our results on Cases 2, 8 and 11, and thinking of the great pleasure we had in the afternoon with the extra­ ordinarily elegant new solution for Case 11, it seemed to me appropriate to pause for a few minutes and dictate a
出版日期Book 1974
关键词Mehrfarbenproblem; boundary element method; form; proof; theorem; topology
版次1
doihttps://doi.org/10.1007/978-3-642-65759-7
isbn_softcover978-3-642-65761-0
isbn_ebook978-3-642-65759-7Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1974
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Graph Theory,Proper formulation of the map Color Problem and the Thread Problem and their solution requires some graph theoretical preparations.
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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 [81] or M. Fréchet and Ky Fan [22].
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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.
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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.
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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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