摘要：Let G be a bridgeless cubic graph and θ = {C1,C2,… ,CK} be a cycle cover of G. Define a new graph G(θ) = (V,E), where V = {C1 ,C2,... ,Ck} ,(Ci ,Cj) ∈ Eif and only if E(Ci) ∩ E(Cj) ≠φ(1 ≤i≠j≤k). Then G is 3-edge colorable if and only if G has a cycle (1,2)-cover θ such that G(θ) is 2 or 3-colorable,which gives a way to verify a bridgeless cubic graph to be 3-edge colorable.%設G是無割邊三正則圖,θ={C1,C2,…,Ck}是G一個圈覆蓋,定義一新圖G(θ)=(V,E),這里V={C1,C2,…,Ck},(Ci,Cj)∈E當且僅當E(Ci)∩ E(Cj)≠φ(1≤i≠j≤k).那么G是三邊著色的充分必要條件是G有一個圈的一或二次覆蓋θ并且G(θ)是二或三點著色.這個結論給出了一個判定無割邊三正則圖是三邊著色的方法.
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