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- W2022757574 abstract "Let G be a simple 3-connected graph with at least five vertices. Tutte [13] showed that G has at least one contractible edge. Thomassen [11] gave a simple proof of this fact and showed that contractible edges have many applications. In this paper, we show that there are at most $frac{|V(G)|}{5}$ vertices that are not incident to contractible edges in a 3-connected graph G. This bound is best-possible. We also show that if a vertex v is not incident to any contractible edge in G, then v has at least four neighbours having degree three, and each such neighbour is incident to exactly two contractible edges. We give short proofs of several results on contractible edges in 3-connected graphs as well. We also study the contractible elements for k-connected matroids. We partially solve an open problem for regular matroids." @default.
- W2022757574 created "2016-06-24" @default.
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- W2022757574 date "2003-07-01" @default.
- W2022757574 modified "2023-09-23" @default.
- W2022757574 title "Contractible Elements in Graphs and Matroids" @default.
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- W2022757574 doi "https://doi.org/10.1017/s0963548302005497" @default.
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