H-colouring bipartite graphs

@article{Engbers2012HcolouringBG,
  title={H-colouring bipartite graphs},
  author={John Engbers and David Galvin},
  journal={J. Comb. Theory, Ser. B},
  year={2012},
  volume={102},
  pages={726-742}
}
For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k ∈ V (H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main result concerns this quantity when G is regular and bipartite. We find numbers 0 ≤ a−(k) ≤ a+(k) ≤ 1 with… CONTINUE READING

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