2021/04/01 by Campo, Eduardo Rivera
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.00481
For a 2-connected graph G and vertices u,v of G we define an abstract graph P(Guv) whose vertices are the paths joining u and v in G, where paths S and T are adjacent if T is obtained from S by replacing a subpath Sxy of S with an internally disjoint subpath Txy of T. We prove that P(Guv) is always connected and give a necessary and a sufficient condition for connectedness in cases where the cycles formed by the replacing subpaths are restricted to a specific family of cycles of G.