On constructible graphs, infinite bridged graphs and weakly cop-win graphs
It is proved that all Helly graphs and connected bridged graphs are constructible. New characterizations of bridged graphs have been deduced. It is also proved that any connected bridged graph is `moorable', a property which implies various fixed point properties. Further, a problem of Hahn et al. has been solved by proving that any finite subgraph of a bridged (resp. constructible) graph \(G\) is contained in a finite induced subgraph \(K\) of \(G\) which is bridged (resp. constructible). It is also shown that the vertex set of \(K\) is a geodesically convex subset of \(V(G)\) whenever \(G\) is locally finite or contains no infinite paths. Some relations between constructible graphs and a weakening of the concept of cop-win graph have been studied.
scientific article; zbMATH DE number 1533339