Abstract
Let G be a 5-connected K 1, d -free graph on n vertices. We show that G contains a 3-connected spanning subgraph of maximum degree at most 2 d â 1. Using an earlier result of ours, we deduce that G contains a cycle of length at least 1 2 n c where c = (log 2 6 + 2 log 2 (2 d â 1)) â1 .
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