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- W3150646944 abstract "For a $2$-connected graph $G$ and vertices $u,v$ of $G$ we define an abstract graph $mathcal{P}(G_{uv})$ whose vertices are the paths joining $u$ and $v$ in $G$, where paths $S$ and $T$ are adjacent if $T$ is obtained from $S$ by replacing a subpath $S_{xy}$ of $S$ with an internally disjoint subpath $T_{xy}$ of $T$. We prove that $mathcal{P}(G_{uv})$ is always connected and give a necessary and a sufficient condition for connectedness in cases where the cycles formed by the replacing subpaths are restricted to a specific family of cycles of $G$." @default.
- W3150646944 created "2021-04-13" @default.
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- W3150646944 date "2021-04-01" @default.
- W3150646944 modified "2023-09-27" @default.
- W3150646944 title "Graph of uv-paths in 2-connected graphs" @default.
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