On the reconstruction of graphs of connectivity $2$ having a $2$-vertex set dividing this graph into at least $3$ parts
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 124-151
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Recall that the deck of a graph $G$ is the collection of subgraphs $G-v$ for all vertices $v$ of the graph $G$. Let $G$ be a of a $2$-connected graph having a $2$-vertex set dividing this graph into at least $3$ parts. We prove that $G$ is reconstructible by its deck. The proof contains an algorithm of the reconstruction.
@article{ZNSL_2022_518_a3,
author = {D. V. Karpov},
title = {On the reconstruction of graphs of connectivity $2$ having a $2$-vertex set dividing this graph into at least $3$ parts},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {124--151},
publisher = {mathdoc},
volume = {518},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a3/}
}
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%0 Journal Article %A D. V. Karpov %T On the reconstruction of graphs of connectivity $2$ having a $2$-vertex set dividing this graph into at least $3$ parts %J Zapiski Nauchnykh Seminarov POMI %D 2022 %P 124-151 %V 518 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a3/ %G ru %F ZNSL_2022_518_a3
D. V. Karpov. On the reconstruction of graphs of connectivity $2$ having a $2$-vertex set dividing this graph into at least $3$ parts. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 124-151. http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a3/