import bpy, bmesh
from mathutils import Vector

def straight(n1,n2,mid):
    v1 = Vector(n1.co-mid.co)
    v2 = Vector(n2.co-mid.co)
    
    if v1.length>0 and v2.length > 0:
        scangle = v1*v2/v1.length/v2.length
        if scangle < -0.85:
            return True
    return False

def follow(v):
    v.select = True
    neighbours = [e.other_vert(v) for e in v.link_edges]
    newn = [n for n in neighbours if  not n.select]
    known = [n for n in neighbours if n.select]

    if len(known) == 1:
        print(v,1)
        next = [n for n in newn if straight(known[0],n,v)]
        print(next)
    elif len(known) > 1:
        print(">1")
        next = []
        print(next)
    else:
        print(0)
        next = [n for n in newn if any([straight(nn,n,v) for nn in newn if nn != n])]
        print(next) 
      
    if len(next) == 1:
        follow(next[0])
    elif len(known) == 0 and len(next) == 2:
        follow(next[0])
        follow(next[1])

obj = bpy.context.object
bm = bmesh.new()
bm.from_mesh(obj.data)

vs = [v for v in bm.verts if v.select]
for v in vs:
    follow(v)

bm.to_mesh(obj.data)