Connectedness and Hamiltonicity of graphs on vertex colorings
Abstract
Given a graph H, let Gjk(H) be the graph whose vertices are the proper k-colorings of H, with edges joining two colorings if H contains a connected subgraph on at most j vertices that includes all vertices where the colorings differ. Properties of G1k(H) have been investigated before, including connectedness and Hamiltonicity. We introduce and study the parameters gk(H) and hk(H), which denote the minimum j such that Gjk(H) is connected or Hamiltonian, respectively.
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