| Abstrakt: | Snark is a bridgeless undirected cubic graph whose edges cannot be coloured with three colours so that no two adjacent edges have the same colour. Sometimes, we do not require each edge to be incident with precisely two vertices but instead, allow even one or none. Structures allowing this are called multipoles and can be joined together through junctions, forming larger multipoles and even graphs. In our work, we explore the colouring properties of proper (2,3)-poles, a specific type of multipole with five dangling edges, that is edges that are incident with only one vertex. They result from snarks by removing a vertex and severing an edge, not incident with the removed vertex. To conduct our analysis, we explore all proper (2,3)-poles resulting from nontrivial snarks with girth at least five and with at most 28 vertices. This encompasses a total of 3,247 snarks and 3,476,400 proper (2,3)-poles. In our research, we provide various structures that can be utilized to expand the colourability of proper (2,3)-poles. In the core of our work, we provide theorems regarding the colouring properties of proper (2,3)-poles, specifically necessary and sufficient conditions for these properties. Additionally, we present the data and observations from the analysis, along with some problems for further research.
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