I am trying to find the set of (surjective) homomorphic images of the Groetzsch Graph - G. I have two ideas, but I am stuck at both. Help with either would be very much appreciated.
1.I try narrowing down the candidate homomorphic images to graphs with chromatic number at least 4 and number of vertices at most 10 in house of graphs. Then i get a graph6 file and try to check if each of those graphs is a homomorphic image of G. This doesn't work because I don't know how exactly to import the graph6 file into sage.
2. Find the independent sets of G and find all the ways I can combine them into homomorphic images. I' ve heard that this is possible, but seems like a rather daunting task for me because I am very new with sage.
