Geodesic
Rooted prism-minors and disjoint cycles containing a specified edge
J.P. Costalonga1 ; T.J. Reid2 ; H. Wu2
1Universidade Estadual de Maringá
2University of Mississipi
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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Dirac and Lovász independently characterized the $3$-connected graphs with no pair of vertex-disjoint cycles. Equivalently, they characterized all $3$-connected graphs with no prism-minors. In this paper, we completely characterize the $3$-connected graphs with no edge that is contained in the union of a pair of vertex-disjoint cycles. As applications, we answer the analogous questions for edge-disjoint cycles and for $4$-connected graphs and we completely characterize the $3$-connected graphs with no prism-minor using a specified edge.
DOI : 10.37236/10198
Classification : 05C40, 05C75, 05C83
Mots-clés : edge-disjoint cycles, Menger's theorem

J.P. Costalonga  1   ; T.J. Reid  2   ; H. Wu  2

1 Universidade Estadual de Maringá
2 University of Mississipi 
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     author = {J.P. Costalonga and T.J. Reid and H. Wu},
     title = {Rooted prism-minors and disjoint cycles containing a specified edge},
     journal = {The electronic journal of combinatorics},
     year = {2023},
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     number = {2},
     doi = {10.37236/10198},
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J.P. Costalonga; T.J. Reid; H. Wu. Rooted prism-minors and disjoint cycles containing a specified edge. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/10198

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