Graph Theoretical Properties of Arcs in the Plane and Fashoda Meet Theorem

Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Graph Theoretical Properties of Arcs in the Plane and Fashoda Meet Theorem

Yatsuka Nakamura: Shinshu University, Nagano

Summary.

We define a graph on an abstract set, edges of which are pairs of any two elements. For any finite sequence of a plane, we give a definition of nodic, which means that edges by a finite sequence are crossed only at terminals. If the first point and the last point of a finite sequence differs, simpleness as a chain and nodic condition imply unfoldedness and s.n.c. condition. We generalize Goboard Theorem, proved by us before, to a continuous case. We call this Fashoda Meet Theorem, which was taken from Fashoda incident of 100 years ago.

MML Identifier: JGRAPH_1

The terminology and notation used in this paper have been introduced in the following articles [32] [10] [36] [3] [33] [20] [37] [8] [9] [4] [11] [16] [1] [2] [21] [28] [25] [35] [26] [19] [27] [29] [24] [23] [18] [6] [14] [5] [15] [22] [30] [34] [13] [12] [31] [17] [7]

Contents (PDF format)

A Graph by Cartesian Product
Shortcuts of Finite Sequences in Plane
Norm of Points in ${\calE}^{n}_{\rmT}$
Extended Goboard Theorem and Fashoda Meet Theorem

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Received August 21, 1998

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