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- W2049076355 abstract "Let G be a graph and let x be a vertex of degree four with NG(x)={a,b,c,d}. Then the operation of deleting x and adding the edges ab and cd is called splitting at x. An edge e of a graph G is said to be k-contractible if contraction of e yields a k-connected graph. Splitting has been studied as a reduction method to preserve edge-connectivity. In this paper, we consider splitting and 4-contractible edges as tools for reduction of 4-connected graphs. We prove that for a 4-connected graph G of order at least six, there exists either a 4-contractible edge or a vertex eligible for splitting preserving 4-connectedness near every vertex in G." @default.
- W2049076355 created "2016-06-24" @default.
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- W2049076355 date "2003-07-01" @default.
- W2049076355 modified "2023-09-27" @default.
- W2049076355 title "Splitting and contractible edges in 4-connected graphs" @default.
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- W2049076355 doi "https://doi.org/10.1016/s0095-8956(02)00043-6" @default.
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