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## Appendix BSnarks, Petersen graph

Methods developed for 3-edge-colorings of cubic graphs play a central role in the study of circuit cover problems. In this chapter, we present some elementary and commonly used results, and methods in this subject.

### B.1 3-edge-coloring of cubic graphs, snarks

The subject of 3-edge-colorings of cubic graphs has been extensively studied in graph theory because of its close relation with the map 4-coloring problem.

Theorem B.1.1 (Tait [220]) Every bridgeless planar graph is 4-face colorable if and only if every bridgeless, cubic, planar graph is 3-edge-colorable.

Proof See Theorem 9.12 of [18], or Theorem 11.4 of [19].

Theorem B.1.2 (The 4-Color Theorem, Appel and Haken [5], [7], [6] and [197], [224]) Every bridgeless ...

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