Tiger Graph

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Definition: A Tiger Graph is a is a finite, 4-valent, directed, edge 2-colored graph where each vertex has one in-edge and one out-edge of each color.

Remark: Because of the above restrictions placed on the tiger graphs, for any given tiger graph, if each edge-coloring is examined separately it will fall into directed simple disjoint cycles.

Theorem: There is a bijection between the set of all tiger graphs and the set of all bipartite dessins.

This tiger graph has three vertices (1,2 and 3), the edge 2-coloring is represented by dotted lines and full lines and the direction is represented by the arrow at the end of each edge