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Path extensibility of connected, locally 2-connected \(K_{1,3}\)-free graphs. (English) Zbl 0891.05047

It is known that every connected, locally 2-connected claw-free graph is panconnected. The authors improve on this result by showing that such a graph is path extendable. That is, for each pair of vertices \(u\), \(v\) and for each non-Hamiltonian \((u,v)\)-path, there is \((u,v)\)-path containing the vertices of \(P\) that is longer by one edge.

MSC:

05C38 Paths and cycles
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