Consequences of an algorithm for bridged graphs

Chepoi showed that every breadth /rst search of a bridged graph produces a cop-win ordering of the graph. We note here that Chepoi’s proof gives a simple proof of the theorem that G is bridged if and only if G is cop-win and has no induced cycle of length four or /ve, and that this characterization together with Chepoi’s proof reduces the time complexity of bridged graph recognition. Speci/cally, we show that bridged graph recognition is equivalent to (C4; C5)-free graph recognition, and reduce the best known time complexity from O(n) to O(n). c © 2003 Elsevier B.V. All rights reserved.