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- W2142831679 abstract "An edge of a 5-connected graph is said to be contractible if the contraction of the edge results in a 5-connected graph. A 5-connected graph with no contractible edge is said to be contraction critically 5-connected. Let G be a contraction critically 5-connected graph and let H be a component of the subgraph induced by the set of degree 5 vertices of G. Then it is known that |V(H)|⩾4. We prove that if |V(H)|=4, then H≅K4−, where K4− stands for the graph obtained from K4 by deleting one edge. Moreover, we show that either |NG(V(H))|=5 or |NG(V(H))|=6 and around H there is one of two specified structures called a K4−-configuration and a split K4−-configuration." @default.
- W2142831679 created "2016-06-24" @default.
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- W2142831679 date "2006-07-01" @default.
- W2142831679 modified "2023-09-25" @default.
- W2142831679 title "Subgraph induced by the set of degree 5 vertices in a contraction critically 5-connected graph" @default.
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- W2142831679 doi "https://doi.org/10.1016/j.endm.2006.06.005" @default.
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