Regular Article
Almost All 3-Connected Graphs Contain a Contractible Set of k Vertices

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Abstract

McCuaig and Ota conjectured that every sufficiently large 3-connected graph G contains a connected subgraph H on k vertices such that GV(H) is 2-connected. We prove the weaker statement that every sufficiently large 3-connected graph G contains a not necessarily connected subgraph H on k vertices such that GV(H) is 2-connected.

Keywords

connectivity
contractable subgraph
reduction
longest induced path
longest cycle

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