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Tietze's graph
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges.
It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regions that all touch each other – three along the boundary of the strip and three along its center line – and therefore that graphs that are embedded onto the Möbius strip may require six colors.〔.〕 The boundary segments of the regions of Tietze's subdivision (including the segments along the boundary of the Möbius strip itself) form an embedding of Tietze's graph.
==Relation to Petersen graph==
Tietze's graph may be formed from the Petersen graph by replacing one of its vertices with a triangle.
Like the Tietze graph, the Petersen graph forms the boundary of six mutually touching regions, but on the projective plane rather than on the Möbius strip. If one cuts a hole from this subdivision of the projective plane, surrounding a single vertex, the surrounded vertex is replaced by a triangle of region boundaries around the hole, giving the previously described construction of the Tietze graph.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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