In this paper we propose a new approach to superposition of snarks, a powerful method of constructing large cubic graphs with no 3-edge-colouring from small ones. The main idea is to use surjective mappings between graphs similar to graph homomorphisms and to control flows induced from the domain graph to the target graph via the mappings. This leads to significant strengthening of the power of the classical superposition, which we illustrate by several examples and two applications. First, we describe a family of cyclically 5-edge-connected snarks $G_d$ of order $3\cdot 2^d-2$, with $d\ge 2$, each being spanned by the balanced cubic tree of depth $d$; the family contains the Petersen graph as $G_2$. The existence of such a family was conjectured by Hoffmann-Ostenhof and Jatschka (2017). Second, we construct cyclically 5-edge-connected permutation snarks of order $n$ for each $n\equiv 2(mod8)$ with $n\ge 34$. Our construction employs a rather exotic form of superposition where the proof of uncolourability of the resulting graph requires two graphs derived from the target graph to be snarks rather than just the target graph itself.

在本文中，我们提出了一种新的蛇形图叠加方法，这是一种构造大型立方图的有效方法，该图没有小边的3边色。主要思想是在图之间使用类似于图同态的射影映射，并控制通过映射从域图到目标图的诱导流。这导致经典叠加功能的显着增强，我们将通过几个示例和两个应用来说明这一点。首先，我们描述一个循环的5边连接的蛇$G_d$ 顺序 $3\cdot 2^d-2$，带有 $d\ge 2$，每个都由平衡的深度立方树跨越 $d$; 家庭包含Petersen图为$G_2$。Hoffmann-Ostenhof和Jatschka（2017）推测了这样一个家庭的存在。其次，我们构造循环的5边连接置换排列$ñ$ 每个 $ñ\equiv 2（模8）$ 与 $ñ\ge 34$。我们的构造采用了一种相当奇特的叠加形式，其中所得图的不可着色性的证明要求从目标图派生的两个图成为蛇形图，而不仅仅是目标图本身。