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- W4246784859 abstract "Peripheral cycles (induced non-separating cycles) in a general 3-connected graph are analogous to the faces of a polyhedron. Using the works of various authors, this paper explores the distribution of contractible edges in 3-connected graphs as needed to prove a major result originally by Tutte: each edge in a 3-connected graph is part of at least 2 peripheral cycles that share only the edge and its end vertices. A complete, alternative proof of this theorem is provided. The inductive step is generalized into a new independent lemma, which states that each edge in a 3-connected graph with a non-adjacent contractible edge has at least as many peripheral cycles as in the contracted one." @default.
- W4246784859 created "2022-05-12" @default.
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- W4246784859 date "2021-07-03" @default.
- W4246784859 modified "2023-10-14" @default.
- W4246784859 title "Contractible Edges and Peripheral Cycles in 3-Connected Graphs" @default.
- W4246784859 doi "https://doi.org/10.47611/jsr.v10i2.1193" @default.
- W4246784859 hasPublicationYear "2021" @default.
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