Geodesic
On semi-reconstruction of graphs of connectivity $2$
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 80-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $G$. We prove that at most two graphs of connectivity $2$ and minimal degree at least $3$ can have the same deck. Let $\mathcal{D}(G)$ be a deck of a $2$-connected graph $G$. We describe an algorithm which construct by the deck $\mathcal{D}(G)$ of a $2$-connected graph $G$ with minimal degree at least $3$ two graphs $G_1,G_2$ such that $G\in \{G_1,G_2\}$. 
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     author = {D. V. Karpov},
     title = {On semi-reconstruction of graphs of connectivity~$2$},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a3/}
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D. V. Karpov. On semi-reconstruction of graphs of connectivity $2$. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 80-99. http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a3/

[1] P. J. Kelly, “A congruence theorem for trees”, Pacific J. Math., 7 (1957), 961–968 | DOI | MR | Zbl

[2] S. M. Ulam, A Collection of Mathematical Problems, Wiley, New York, 1960 | MR

[3] W. T. Tutte, Connectivity in Graphs, Univ. Toronto Press, Toronto, 1966 | MR | Zbl

[4] J. A. Bondy, “On Ulam's conjecture for separable graphs”, Pacific J. Math., 31 (1969), 281–288 | DOI | MR | Zbl

[5] Y. Yongzhi, “The reconstruction conjecture is true if all $2$-connected graphs are reconstructible”, J. Graph Theory, 12 (1988), 237–243 | DOI | MR | Zbl

[6] D. V. Karpov, A. V. Pastor, “$k$-connected graph”, J. Math. Sci., 113:4 (2003), 584–597 | DOI | MR

[7] D. V. Karpov, “Blocks in $k$-connected graphs”, J. Math. Sci., 126:3 (2005), 1167–1181 | DOI | MR

[8] D. V. Karpov, “Cutsets in a $k$-connected graph”, J. Math. Sci., 145:3 (2007), 4953–4966 | DOI | MR

[9] D. V. Karpov, “The Decomposition Tree of a Biconnected Graph”, J. Math. Sci., 204:2 (2015), 232–243 | DOI | MR | Zbl

[10] D. V. Karpov, “Minimal biconnected graphs”, J. Math. Sci., 204:2 (2015), 244–257 | DOI | MR | Zbl

[11] D. V. Karpov, “Decomposition of a $2$-connected graph into three connected subgraphs”, J. Math. Sci., 236:5 (2019), 490–502 | DOI | MR | Zbl

[12] D. V. Karpov, “Large contractible subgraphs of a $3$-connected graph”, Discussiones Mathematicae Graph Theory (to appear) | DOI | MR