Abstract.
Suppose that is the set of connected graphs such that a graph G∈ if and only if G satisfies both (F1) if X is an edge cut of G with |X|≤3, then there exists a vertex v of degree |X| such that X consists of all the edges incident with v in G, and (F2) for every v of degree 3, v lies in a k-cycle of G, where 2≤k≤3.
In this paper, we show that if G∈ and κ′(G)≥3, then for every pair of edges e,f∈E(G), G has a trail with initial edge e and final edge f which contains all vertices of G. This result extends several former results.
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Lai, HJ., Li, X., Poon, H. et al. Spanning Trails Connecting Given Edges. Graphs and Combinatorics 21, 77–88 (2005). https://doi.org/10.1007/s00373-004-0579-7
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DOI: https://doi.org/10.1007/s00373-004-0579-7