Open problems on graphs arising from geometric topology

AbstractWe have collected several open problems on graphs which arise in geometric topology, in particular in the following areas: 1.(1) basic embeddability of compacta into the plane R2;2.(2) approximability of maps by embeddings;3.(3) uncountable collections of continua in R2 and their span; and4.(4) representations of closed PL manifolds by colored graphs. These problems should be of interest to both topologists and combinatorists