A Course in Topological Combinatorics by Mark de Longueville

Author:Mark de Longueville [Longueville, Mark de]
Language: eng
Format: epub, pdf
Tags: Applied, Graphic Methods, Analytic, Algebraic, Geometry, General, Combinatorics, Mathematics, Game Theory, Topology
ISBN: 9781441979100
Google: L3KMSTHvigwC
Publisher: Springer Science & Business Media
Published: 2011-01-02T00:00:00+00:00

Fig. 4.33Splitting the path in the essential part

Therefore, if i and j are even, then we are done. Otherwise, either i or j is odd, or both. We will consider separately the cases in which precisely one of them is odd and in which both are odd.

In the first case, we may assume that i is even and j is odd. We will construct a thrackle drawing of 8 i, 2j . Lemma 4.36 tells us that the drawings of the two cycles C i and C j touch at the common vertex x. We will double the cycle C j in a two-step procedure depicted in Fig. 4.34. First the path of even length j − 1 along C j is doubled using the doubling of edges as before, and then the crossing at the vertex x is modified as shown in the second step.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.